K. C. Sinha Solutions for Chapter: Area Enclosed by Curves, Exercise 1: EXERCISE

In what ratio does the $x$-axis divide the area of the region bounded by the parabolas $y=4x-x^2$ and $y=x^2-x?$

Find the ratio in which the area bounded by the curves $y^2=12x$ and $x^2=12y$ is divided by the line $x=3.$

Find the area enclosed by the curves $3x^2+5y=32$ and $y=\left|x-2\right|.$

Find the area bounded by the curve $\left|y\right|+\frac{1}{2}\le e^{-\left|x\right|}.$

Find the value of $t$ for which the area bounded by the lines $y=0, x=0, x=1$ and the curve $y=t^2{x}^2+tx+1$ is minimum.

Find the area bounded by the curves $y=\log x$ and $y={\left(\log x\right)}^2.$

Sketch the smallest of the regions bounded by the curves $x^2+4y^2-2x-8y+1=0$ and $4y^2-3x-8y+7=0.$ Find its area.

For the figure bounded by the curves $y^m=x^n$ and $y^n=x^m,$ where $m$ and $n$ are positive integers, find the area of the portion situated in the first quadrant. Consider the area of the entire figure depending on whether $m$ and $n$ are even or odd.