K. C. Sinha Solutions for Chapter: Area Enclosed by Curves, Exercise 2: EXERCISE

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 $\left(\sqrt{a^2+1}-\sqrt{2}\right)$ sq. unit for all $a>1 \left(f\left(x\right)>0\right).$ Then which of the following are true:

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

Let $f\left(x\right)=\min \left\{\tan x, \cot x, \frac{1}{\sqrt{3}}\right\} \forall x\in \left[0,\frac{\mathrm{\pi }}{2}\right]$. If the area bounded by $y=f\left(x\right)$ and $x$-axis is $\ln \left(\frac{a}{b}\right)+\frac{\mathrm{\pi }}{6\sqrt{3}}$ sq. units, where $a$ and $b$ are co-prime, then $ab$ is equal to

If the area bounded by $4y=\left|4-x^2\right|$ and $y=7-\left|x\right|$ is $k$ square units, then $k$ is equal to

If $∆$ be the area between the curve $y=x^2+x-2$ and $y=2x$ for which $\left|x^2+x-2\right|+\left|2x\right|=\left|x^2+3x-2\right|$ is satisfied, then $9∆$ is equal to

Let $f\left(x\right)=\min \left[\tan x, \cot x, \frac{1}{\sqrt{3}}\right], x\in \left[0,\frac{\mathrm{\pi }}{2}\right]$. If the area bounded by $y=f\left(x\right)$ and $x$-axis is $\ln \left(\frac{a}{b}\right)+\frac{\mathrm{\pi }}{6\sqrt{3}}$(in sq. units), where $a, b$ are co-primes. Then $ab=$

The maximum area bounded by the curves $y^2=4ax, y=ax$ and $y=\frac{x}{a}, 1 \le a\le 2$ in squares units is equal to