Area Bounded by Curves

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JEE Main 2016

The area (in sq. units) of the region ${(x, y) : y^{2} \geq 2 x and x^{2} + y^{2} \leq 4 x, x \geq 0, y \geq 0}$ is:

π - \frac{4 2}{3}

(B)

\frac{π}{2} - \frac{2 2}{3}

(C)

π - \frac{4}{3}

(D)

π - \frac{8}{3}

JEE Main 2015

LEVELJEE Main

The area (in sq. units) of the region described by ${(x, y) : y^{2} \leq 2 x and y \geq 4 x - 1}$ is

The area of the region described by $A = {(x, y) : x^{2} + y^{2} \leq 1 and y^{2} \leq 1 - x}$ is:

(A)

\frac{π}{2} - \frac{2}{3}

(B)

\frac{π}{2} + \frac{2}{3}

(C)

\frac{π}{2} + \frac{4}{3}

(D)

\frac{π}{4} - \frac{2}{3}

JEE Main 2013

LEVELJEE Main

The area (in square units) bounded by the curves $y = x, 2 y - x + 3 = 0$ , x-axis, and lying in the first quadrant is:

The area between the parabolas $x^{2} = \frac{y}{4}$ and $x^{2} = 9 y$ and the straight line $y = 2$ is:

(A)

202

(B)

\frac{10 2}{3}

(C)

\frac{20 2}{3}

(D)

102

JEE Main 2011

LEVELJEE Main

The area of the region enclosed by the curves $y = x, x = e, y = 1/ x$ and the positive x-axis is

The area bounded by the curves $y = cos x$ and $y = sin x$ between the ordinates $x = 0$ and $x = \frac{3 π}{2}$ is

(A)

42 + 2

(B)

42 - 1

(C)

42 + 1

(D)

42 - 2

JEE Main 2009

LEVELJEE Main

The area of the region bounded by the parabola $(y - 2)^{2} = x - 1$ , the tangent of the parabola at the point (2, 3) and the x-axis is:

The area of the plane region bounded by the curves $x + 2 y^{2} = 0$ and $x + 3 y^{2} = 1$ is equal to

The area enclosed between the curves $y^{2} = x$ and $y = ∣ x ∣$ is

The area enclosed between the curve $y = lo g_{e} (x + e)$ and the coordinate axes is

The parabolas $y^{2} = 4 x$ and $x^{2} = 4 y$ divide the square region bounded by the lines $x = 4, y = 4$ and the coordinate axes. If $S_{1}, S_{2}, S_{3}$ are respectively the areas of these parts numbered from top to bottom; then $S_{1} : S_{2} : S_{3}$ is

Let $f (x)$ be a non-negative continuous function such that the area bounded by the curve $y = f (x)$ , x-axis and the ordinates $x = π /4$ and $x = β > π /4$ is $[β sin β + \frac{π}{4} cos β + 2 β]$ . Then $f (π /2)$ is

(A)

(\frac{π}{4} + 2 - 1)

(B)

(\frac{π}{4} - 2 + 1)

(C)

(1 - \frac{π}{4} - 2)

(D)

(1 - \frac{π}{4} + 2)

JEE Main 2004

LEVELJEE Main

The area of the region bounded by the curves $y = ∣ x - 2∣, x = 1, x = 3$ and the x-axis is

The area of the region bounded by the curves $y = ∣ x - 1∣$ and $y = 3 - ∣ x ∣$ is

The area bounded by the curves $y = ln x, y = ln ∣ x ∣, y = ∣ ln x ∣$ and $y = ∣ ln ∣ x ∣∣$ is

Area of the region ${(x, y) \in R^{2} : y \geq ∣ x + 3∣, 5 y \leq x + 9 \leq 15}$ is equal to

The area enclosed by the curves $y = sin x + cos x$ and $y = ∣ cos x - sin x ∣$ over the interval $[0, π /2]$ is

(A)

4 (2 - 1)

(B)

22 (2 - 1)

(C)

2 (2 + 1)

(D)

22 (2 + 1)

JEE Advanced 2012

LEVELJEE Advanced

Let $S$ be the area of the region enclosed by $y = e^{- x^{2}}, y = 0, x = 0$ and $x = 1$ ; then

* Multiple Correct Options

(A)

S \geq \frac{1}{e}

(B)

S \geq 1 - \frac{1}{e}

(C)

S \leq \frac{1}{4} (1 + \frac{1}{e})

(D)

S \leq \frac{1}{2} + \frac{1}{e} (1 - \frac{1}{2})

JEE Advanced 2011

LEVELJEE Main

Let the straight line $x = b$ divide the area enclosed by $y = (1 - x)^{2}$ , $y = 0$ , and $x = 0$ into two parts $R_{1} (0 \leq x \leq b)$ and $R_{2} (b \leq x \leq 1)$ such that $R_{1} - R_{2} = 1/4$ . Then $b$ equals

Area of the region bounded by the curve $y = e^{x}$ and lines $x = 0$ and $y = e$ is

* Multiple Correct Options

(A)

e - 1

(B)

\int_{1}^{e} ln (e + 1 - y) d y

(C)

e - \int_{0}^{1} e^{x} d x

(D)

\int_{1}^{e} ln y d y

JEE Advanced 2008

LEVELJEE Advanced

The area of the region between the curves $y = \frac{1 + s i n x}{c o s x}$ and $y = \frac{1 - s i n x}{c o s x}$ bounded by the lines $x = 0$ and $x = π /4$ is

(A)

\int_{0}^{2 - 1} \frac{t}{( 1 + t ^{2} ) 1 - t ^{2}} d t

(B)

\int_{0}^{2 - 1} \frac{4 t}{( 1 + t ^{2} ) 1 - t ^{2}} d t

(C)

\int_{0}^{2 + 1} \frac{4 t}{( 1 + t ^{2} ) 1 - t ^{2}} d t

(D)

\int_{0}^{2 + 1} \frac{t}{( 1 + t ^{2} ) 1 - t ^{2}} d t

JEE Advanced 2005

LEVELJEE Main

The area bounded by the parabolas $y = (x + 1)^{2}$ and $y = (x - 1)^{2}$ and the line $y = 1/4$ is

The area enclosed between the curves $y = a x^{2}$ and $x = a y^{2}$ ( $a > 0$ ) is 1 sq. unit, then the value of $a$ is

(A)

1/ 3

(B)

1/2

(C)

(D)

1/3

JEE Advanced 2003

LEVELJEE Main

The area bounded by the curves $y = x$ , $2 y + 3 = x$ and x-axis in the 1st quadrant is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area (in sq. units) of the region {(x,y):y2≥2x and x2+y2≤4x,x≥0,y≥0} is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area (in sq. units) of the region described by {(x,y):y2≤2x and y≥4x−1} is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of the region described by A={(x,y):x2+y2≤1 and y2≤1−x} is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area (in square units) bounded by the curves y=x​,2y−x+3=0, x-axis, and lying in the first quadrant is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area between the parabolas x2=4y​ and x2=9y and the straight line y=2 is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of the region enclosed by the curves y=x,x=e,y=1/x and the positive x-axis is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area bounded by the curves y=cosx and y=sinx between the ordinates x=0 and x=23π​ is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of the region bounded by the parabola (y−2)2=x−1, the tangent of the parabola at the point (2, 3) and the x-axis is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of the plane region bounded by the curves x+2y2=0 and x+3y2=1 is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area enclosed between the curves y2=x and y=∣x∣ is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area enclosed between the curve y=loge​(x+e) and the coordinate axes is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of the region bounded by the curves y=∣x−2∣,x=1,x=3 and the x-axis is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of the region bounded by the curves y=∣x−1∣ and y=3−∣x∣ is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area bounded by the curves y=lnx,y=ln∣x∣,y=∣lnx∣ and y=∣ln∣x∣∣ is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Area of the region {(x,y)∈R2:y≥∣x+3∣​,5y≤x+9≤15} is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area enclosed by the curves y=sinx+cosx and y=∣cosx−sinx∣ over the interval [0,π/2] is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let S be the area of the region enclosed by y=e−x2,y=0,x=0 and x=1; then

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let the straight line x=b divide the area enclosed by y=(1−x)2, y=0, and x=0 into two parts R1​(0≤x≤b) and R2​(b≤x≤1) such that R1​−R2​=1/4. Then b equals

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Area of the region bounded by the curve y=ex and lines x=0 and y=e is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area of the region between the curves y=cosx1+sinx​​ and y=cosx1−sinx​​ bounded by the lines x=0 and x=π/4 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area bounded by the parabolas y=(x+1)2 and y=(x−1)2 and the line y=1/4 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area enclosed between the curves y=ax2 and x=ay2 (a>0) is 1 sq. unit, then the value of a is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The area bounded by the curves y=x​, 2y+3=x and x-axis in the 1st quadrant is

The area (in sq. units) of the region ${(x, y) : y^{2} \geq 2 x and x^{2} + y^{2} \leq 4 x, x \geq 0, y \geq 0}$ is:

The area (in sq. units) of the region described by ${(x, y) : y^{2} \leq 2 x and y \geq 4 x - 1}$ is

The area of the region described by $A = {(x, y) : x^{2} + y^{2} \leq 1 and y^{2} \leq 1 - x}$ is:

The area (in square units) bounded by the curves $y = x, 2 y - x + 3 = 0$ , x-axis, and lying in the first quadrant is:

The area between the parabolas $x^{2} = \frac{y}{4}$ and $x^{2} = 9 y$ and the straight line $y = 2$ is:

The area of the region enclosed by the curves $y = x, x = e, y = 1/ x$ and the positive x-axis is

The area bounded by the curves $y = cos x$ and $y = sin x$ between the ordinates $x = 0$ and $x = \frac{3 π}{2}$ is

The area of the region bounded by the parabola $(y - 2)^{2} = x - 1$ , the tangent of the parabola at the point (2, 3) and the x-axis is:

The area of the plane region bounded by the curves $x + 2 y^{2} = 0$ and $x + 3 y^{2} = 1$ is equal to

The area enclosed between the curves $y^{2} = x$ and $y = ∣ x ∣$ is

The area enclosed between the curve $y = lo g_{e} (x + e)$ and the coordinate axes is

The area of the region bounded by the curves $y = ∣ x - 2∣, x = 1, x = 3$ and the x-axis is

The area of the region bounded by the curves $y = ∣ x - 1∣$ and $y = 3 - ∣ x ∣$ is

The area bounded by the curves $y = ln x, y = ln ∣ x ∣, y = ∣ ln x ∣$ and $y = ∣ ln ∣ x ∣∣$ is

Area of the region ${(x, y) \in R^{2} : y \geq ∣ x + 3∣, 5 y \leq x + 9 \leq 15}$ is equal to

The area enclosed by the curves $y = sin x + cos x$ and $y = ∣ cos x - sin x ∣$ over the interval $[0, π /2]$ is

Let $S$ be the area of the region enclosed by $y = e^{- x^{2}}, y = 0, x = 0$ and $x = 1$ ; then

Let the straight line $x = b$ divide the area enclosed by $y = (1 - x)^{2}$ , $y = 0$ , and $x = 0$ into two parts $R_{1} (0 \leq x \leq b)$ and $R_{2} (b \leq x \leq 1)$ such that $R_{1} - R_{2} = 1/4$ . Then $b$ equals

Area of the region bounded by the curve $y = e^{x}$ and lines $x = 0$ and $y = e$ is

The area of the region between the curves $y = \frac{1 + s i n x}{c o s x}$ and $y = \frac{1 - s i n x}{c o s x}$ bounded by the lines $x = 0$ and $x = π /4$ is

The area bounded by the parabolas $y = (x + 1)^{2}$ and $y = (x - 1)^{2}$ and the line $y = 1/4$ is

The area enclosed between the curves $y = a x^{2}$ and $x = a y^{2}$ ( $a > 0$ ) is 1 sq. unit, then the value of $a$ is

The area bounded by the curves $y = x$ , $2 y + 3 = x$ and x-axis in the 1st quadrant is