Embibe Experts Solutions for Chapter: Application of Integrals, Exercise 1: Exercise 1

Area enclosed by the curve $y=f\left(x\right)$ defined parametrically as $x=\frac{1-t^2}{1+t^2}, y=\frac{2t}{1+t^2}$ is equal to

The area of the loop of the curve $x^2+\left(y-1\right)y^2=0$ is equal to

The area of the region in the first quadrant included between the curves $x^2+y^2=16$ and $\sqrt{\left|x\right|}+\sqrt{\left|y\right|}=2$ is

The area bounded by $y=x{e}^{\left|x\right|}$ and lines $\left|x\right|=1, y=0$ is

The smaller of the areas bounded by the curves $x^2+y^2=4$ and $y^2=2\left(x+2\right)$ is

Area bounded by the parabola $x={\left(y-2\right)}^2+1,$ the tangent to it at the point $P\left(2,3\right)$ and the $x-$axis is equal to

The area bounded by the curves $y=\cos x$ and $y=\sin x$ between the ordinates $x=0$ and $x=\frac{3\pi }{2}$ is 

Let $f\left(x\right)=x^2, g\left(x\right)=\cos x$ and $\alpha ,\beta \left(\alpha <\beta \right)$, the roots of the equation $18x^2-9\pi x+{\pi }^2=0.$ The area bounded by the curve $y=f\left[g\left(x\right)\right]$, the ordinates $x=\alpha , x=\beta$ and the $x$-axis is