Area Under The Curves · Mathematics · MHT CET
MCQ (Single Correct Answer)
If the area bounded by the curve $x^2=4 y, \mathrm{X}$-axis and the line $x=4$ is divided into equal areas by the line $x=\alpha$, then the value of $\alpha$ is …
The area of smaller part between the circle $x^2+y^2=4$ and the line $x=1$ is _________ sq.units.
The area bounded by the curve $y=4 x-x^2$ and X - axis in square units, is $\qquad$
The area bounded by the parabolas $y=9 x^2, y=\frac{x^2}{16}$ and the line $y=1$ is
The area bounded by the curve $y=x^2+3, y=x, x=3$ and $y$-axis is
The area bounded by the curve $x^2=8 y$ and the straight line $x-8 y+2=0$ is
If a curve $y=a \sqrt{x}+b x$ passes through the point $(1,2)$ and the area bounded by this curve, line $x=4$ and the X -axis is 8 sq . units, then the value of $a-b$ is
The area bounded by the curve $x=2-y-y^2$ and the Y -axis is
The area of the region bounded by the curve $y=|x-2|$ between $x=1, x=3$ and X -axis is ……
The area inside the parabola $y^2=4 \mathrm{a} x$, between the lines $x=\mathrm{a}$ and $x=4 \mathrm{a}$ is equal to
The area of the region bounded by $\frac{x^2}{9}+\frac{y^2}{4}=1$ and the line $\frac{x}{3}+\frac{y}{2}=1$ is
The area enclosed between the curves $y^2=4 x$ and $y=|x|$ is
The area (in sq. units) bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9 y$ and the line $y=2$ is
The area (in sq. units) of the region described by $\left\{(x, y) / y^2 \leq 2 x\right.$ and $\left.y \geq(4 x-1)\right\}$ is
The area enclosed between the parabola $y^2=4 x$ and the line $y=2 x-4$ is
The area of the region bounded by curves $y=3 x+1, y=4 x+1$ and $x=2$ is
The area (in sq. units) of the region bounded by $y-x=2$ and $x^2=y$ is equal to
The area of the region lying in the first quadrant by $y=4 x^2, x=0, y=2, y=4$ is
The area (in sq. units) of the region $\left\{(x, y) / x \geq 0, x+y \leq 3, x^2 \leq 4 y\right.$ and $\left.y \leq 1+\sqrt{x}\right\}$ is
Area (in sq.units) lying in the first quadrant and bounded by the circle $x^2+y^2=4$ and the lines $x=0$ and $x=2$ is
The area (in sq. units), in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=2$, is
The area (in sq. units) bounded by the curves $y=(x+1)^2, y=(x-1)^2$ and the line $y=\frac{1}{4}$ is
The area (in square units) in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=3$, is
The area bounded between the curves $y=a x^2$ and $x=a y^2(a>0)$ is 1 sq. units, then the value of a is
The area of the region, bounded by the parabola $y=x^2+2$ and the lines $y=x, x=0$ and $x=3$, is
The area (in sq. units) of the region bounded by the curve $x^2=4 y$ and the straight line $x=4 y-2$ is
The area (in sq. units) bounded by the curves $y=\sqrt{x}, 2 y-x+3=0, X$-axis and lying in the first quadrant is
The area of the region bounded by hyperbola $x^2-y^2=9$ and its latus rectum is
The area bounded by the curve $$y=|x-2|, x=1, x=3$$ and $$X$$-axis is
If $$\mathrm{f}^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2} < x < \frac{\pi}{2}$$ and $$f(0)=0$$, then $$\mathrm{f}(1)$$ is
The area bounded by the curves $$y=(x-1)^2, y=(x+1)^2$$ and $$y=\frac{1}{4}$$ is
If a curve $$y=a \sqrt{x}+b x$$ passes through the point $$(1,2)$$ and the area bounded by the curve, line $$x=4$$ and $$X$$-axis is 8 sq units, then
The area (in sq. units) of the region bounded by curves $$y=3 x+1, y=4 x+1$$ and $$x=3$$ is
The area (in sq. units) of the smaller part of the circle $$x^2+y^2=\mathrm{a}^2$$ cut off by the line $$x=\frac{\mathrm{a}}{\sqrt{2}}$$ is
The area of the region bounded by the curves $$y=\mathrm{e}^x, y=\log x$$ and lines $$x=1, x=2$$ is
The slope of the tangent to a curve $$y=\mathrm{f}(x)$$ at $$(x, \mathrm{f}(x))$$ is $$2 x+1$$. If the curve passes through the point $$(1,2)$$, then the area (in sq. units), bounded by the curve, the $$\mathrm{X}$$-axis and the line $$x=1$$, is
The area of the region bounded by the parabola $$y=x^2$$ and the curve $$y=|x|$$ is
The area bounded by the $$\mathrm{X}$$-axis and the curve $$y=x(x-2)(x+1)$$ is
Area of the region bounded by the curve $$y=\sqrt{49-x^2}$$ and $$\mathrm{X}$$-axis is
If $$\mathrm{f}^{\prime}(x)=x-\frac{5}{x^5}$$ and $$\mathrm{f}(1)=4$$, then $$\mathrm{f}(x)$$ is
The area (in sq. units) bounded by the curve $$y=x|x|, \mathrm{X}$$-axis and the lines $$x=-1$$ and $$x=1$$ is
The area (in sq. units) of the region $$\mathrm{A}=\left\{(x, y) / \frac{y^2}{2} \leq x \leq y+4\right\}$$ is
The area (in sq. units) of the region described by $$A=\left\{(x, y) / x^2+y^2 \leq 1\right.$$ and $$\left.y^2 \leq 1-x\right\}$$ is
The area of the region bounded by the curve $$y=2 x-x^2$$ and X-axis is
Area bounded by the lines $$y=x, x=-1, x=2$$ and the $$X$$-axis is
The area of the region included between the parabolas $$y^2=8 x$$ and $$x^2=8 y$$, is
The area bounded by the parabola $$y^2=4 a x$$ and its latus-rectum $$x=a$$ is
The area bounded by the parabola $$y^2=x$$ and the line $$x+y=2$$ in the first quadrant is
The area bounded between the curve $$x^2=y$$ and the line $$y=4 x$$ is
The area bounded by the parabola $$y^2=x$$, the straight line $$y=4$$ and $$Y$$ axis is
The area of the region bounded by the curve y$$^2$$ = 4x and the line y = x is
The area bounded by the parabola $$y=x^2$$ and the line $$y=x$$ is
The area of the region bounded by the parabola x$$^2$$ = y and the line y = x is
The area of the region bounded by the curve $y=\sin x$ between $x=-\pi$ and $x=\frac{3 \pi}{2}$ is
The area included between the parabolas $$y^2=5 x$$ and $$x^2=5 y$$ is
The area of the region bounded by the curve $$y=4 x^3-6 x^2+4 x+1$$ and the lines $$x=1, x=5$$ and $$X$$-axis is
. Area of the region bounded by $y=\cos x, x=0$, $x=\pi$ and $X$-axis is ... sq. units.
The area of the region enclosed between pair of the lines $x y=0$ and the lines $x y+5 x-4 y-20=0$, is .............
The area of the region bounded by the curve $y=2 x-x^2$ and the line $y=x$ is ........... units. square