Embibe Experts Solutions for Chapter: Definite Integration, Exercise 1: Level 1

What is ${\int }_0^{\frac{\pi }{2}}\frac{dx}{a^2{\cos }^{2}x+b^2{\sin }^{2}x}$ equal to$?$

What is ${\int }_0^{2\pi }\sqrt{1+\sin \frac{x}{2}}dx$ equal to $?$

What is the value ${\int }_{-\pi /4}^{\pi /4}\left(\sin x-\tan x\right)dx ?$

What is ${\int }_0^{1}x{\left(1-x\right)}^{9}dx$ equal to ?

Let $f\left(x\right)$ be a function satisfying $f\left(x\right)=f\left(\frac{100}{x}\right)\forall x>0.$ If ${\int }_1^{10}\frac{f\left(x\right)}{x}dx=5$, then find the value of ${\int }_1^{100}\frac{f\left(x\right)}{x}dx$

The value of ${\int }_{-2}^2\left|3x^2-3x-6\right|dx$ is

The value of $6{\int }_0^3\left|\left(x-1\right)\left(x-2\right)\right|dx$ is equal to

$\underset{n\to \infty }{\lim }\frac{1}{n}\left[1+\frac{n^2}{n^2+1^2}+\frac{n^2}{n^2+2^2}+\dots +\frac{n^2}{n^2+{\left(n-1\right)}^2}\right]$ is equal to