Area under Simple Curves

The area enclosed by ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ above $x$–axis in square units is

Find the area of the region bounded by $x^2=4y, y=2, y=4$ and the $y-$axis in the first quadrant.

If the area of the region bounded by the curve $y=\sin x$, between $x=0$ and $x=2\pi$ is $k$ sq. units, then the value of $k$ is

The maximum possible area bounded by the parabola $y=x^2+x+10$ and a chord of the parabola of length $1$ is

The area bounded by the parabola $x^2=4y$ and line $y=3$ is equal to

If the area in sq.units of the triangle, the equations of whose sides are $y=2x+1, y=3x+1$ and $x=4$ is $k$ sq. units, then the value of $k$ is

Compare the areas under the curves $y={\cos }^{2}x$ and $y={\sin }^{2}x$ between $x=0$ and $x=\pi .$

Find the area[sq.units] bounded by the curve $y=\left(4-x^2\right)$, the $y$-axis and the lines $y=0, y=3$.

If the area in sq.units enclosed by curve $y=x^3$, and the lines $y=0, x=2$ and $x=4$ is $k$, then the value of $k$ is

Area bounded by the curves $y^2=4x$ and $y=2x$ is equal to

The area bounded by the curve $y=f\left(x\right), x-$axis and the ordinates $x=1$ and $x=a$ is $\left(\sqrt{a^2+1}-\sqrt{2}\right)$ for all $a>1 \left(f\left(x\right)>0\right).$ Then

The area bounded by $y=\left|e^{\left|x\right|}-e^{-x}\right|,$ the $x-$axis and $x=1$ is

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

The values of $m$ for which the area of the region bounded by the curve $y=x-x^2$ and the line $y=mx$ is $\frac{9}{2}$ are

The area of the region $\left\{\left(x, y\right):x^2 \le y \le \left|x\right|\right\}$ is 

Area of ellipse $\frac{x^2}{4}+\frac{y^2}{25}=1$ is $k\pi \text{ square unit }$. Find $k$.

Area of circle $x^2+y^2=25$ is $k\pi \text{ square units. }$. Find $k$.

Find the area (in value only) of $∆\mathrm{PQR}$ whose vertices are $\mathrm{P}(2,1),\mathrm{Q}(3,4),$ and $\mathrm{R}(5,2)$

Find the area of the region lying in the first quadrant and bounded by $y=4x^2, x=0, y=1$ and $y = 4.$

Area of the region bounded by the following curve, the $X$ -axis and the given lines$y=\sqrt{16-x^2},x=0,x=4$ is $k\pi \text{ square unit}$. Find $k$.