Engineering Mat...

Let the function f satisfies $f\left(x\right)+2f\left(\frac{1}{x}\right)=x^2,x\ne 0$.

If R is the region 0 ≤ x ≤ y ≤ L, then

$\int \underset{R}{\int }\left(x^2+y^2\right)dxdy$ is

A curve is given by x² + 2y² = 16 is revolved around x axis. The volume of solid generated is

The value of the integral $\underset{0}{\overset{3}{\int }}\frac{2x}{{\left(1-x^2\right)}^{2/3}}dx$ is

A mouse is running on a string whose equation is given by $y=\frac{2}{3}{x}^{3/2}$. The mouse moves along the string from point A whose x-coordinate is 0 to point B where x = 3. Find the distance ran by the mouse.

The value of $\underset{0}{\overset{\frac{\pi }{6}}{\int }}{\cos }^{4}3\theta {\sin }^{3}6\theta \mathrm{d}\theta$ is

If $I=\underset{0}{\overset{2}{\int }}{x}^{\left[x^2\right]}dx$, where [x] denotes greatest integer function. Find I upto 2 decimal places.