# Application of Integration · Mathematics · WB JEE

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## MCQ (Single Correct Answer)

WB JEE 2008
The function f(x) which satisfies $$f(x) = f( - x) = {{f'(x)} \over x}$$ is given by
WB JEE 2008
The area enclosed between the curve y = 1 + x2, the y-axis, and the straight line y = 5 is given by
WB JEE 2008
The line which is parallel to x-axis and crosses the curve y = $$\sqrt x$$ at an angle 45$$^\circ$$ is
WB JEE 2008
The area included between the parabolas y2 = 4x and x2 = 4y is
WB JEE 2008
Select the correct statement from (a), (b), (c), (d). The function $$f(x) = x{e^{1 - x}}$$
WB JEE 2008
The equation ex + x $$-$$ 1 = 0 has, apart from x = 0
WB JEE 2008
The function $$f(x) = {e^{ax}} + {e^{ - ax}},a > 0$$ is monotonically increasing for
WB JEE 2010
The area enclosed by y = 3x $$-$$ 5, y = 0, x = 3 and x = 5 is
WB JEE 2010
The area bounded by the parabolas y = 4x2, $$y = {{{x^2}} \over 9}$$ and the line y = 2 is
WB JEE 2010
The area of the region bounded by y2 = x and y = | x | is
WB JEE 2011
The area enclosed between y2 = x and y = x is
WB JEE 2011
The area bounded by y2 = 4x and x2 = 4y is
WB JEE 2022
If $$x{{dy} \over {dx}} + y = x{{f(xy)} \over {f'(xy)}}$$, then $$|f(xy)|$$ is equal to
WB JEE 2022
Area of the figure bounded by the parabola $${y^2} + 8x = 16$$ and $${y^2} - 24x = 48$$ is
WB JEE 2022
Let f be a non-negative function defined in $$[0,\pi /2]$$, f' exists and be continuous for all x and $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}} dt ... WB JEE 2021 Let f : R$$\to$$R be such that f(0) = 0 and$$\left| {f'(x)} \right| \le 5$$for all x. Then f(1) is in WB JEE 2021 The straight the through the origin which divides the area formed by the curves y = 2x$$-$$x2, y = 0 and x = 1 into two equal halves is WB JEE 2021 The area bounded by the parabolas$$y = 4{x^2},y = {{{x^2}} \over 9}$$and the straight line y = 2 is WB JEE 2020 If$${x^2} + {y^2} = {a^2}$$, then$$\int\limits_0^a {\sqrt {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} dx = } $$WB JEE 2020 Area in the first quadrant between the ellipses x2 + 2y2 = a2 and 2x2 + y2 = a2 is WB JEE 2020 The area of the region$$\{ (x,y):{x^2} + {y^2} \le 1 \le x + y\} $$is WB JEE 2019 Let P and T be the subsets of k, y-plane defined byP = {(x, y) : x > 0, y > 0 and x2 + y2 = 1}T = {(x, y) : x > 0, y > 0 and x8 + y8 < ... WB JEE 2017 The area of the figure bounded by the parabolas x =$$-$$2y2 and x = 1$$-$$3y2 is ## Subjective WB JEE 2008 Solve :$$({x^2} + 4{y^2} + 4xy)dy = (2x + 4y + 1)dx$$## MCQ (More than One Correct Answer) WB JEE 2020 The area of the figure bounded by the parabola$$x = - 2{y^2},\,x = 1 - 3{y^2} is
WB JEE 2019
The area bounded by y = x + 1 and y = cos x and the X-axis, is
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