M L Aggarwal Solutions for Chapter: Integrals, Exercise 20: CHAPTER TEST

$\underset{1}{\overset{e}{\int }}\frac{1+\log x}{2x}dx=$

If $\int \left|x\right|dx=k x\left|x\right|+C$, Then what is the value of $k$ ?

Evaluate $\underset{1}{\overset{3}{\int }} \left(x^2+5x\right)dx$

Evaluate $\underset{0}{\overset{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\int }}\sqrt{\sin x}{\cos }^{5}xdx$.

Evaluate $\underset{0}{\overset{4}{\int }}\left(\left|x\right|+\left|x-2\right|+\left|x-4\right|\right) dx$

Evaluate $\underset{0}{\overset{1}{\int }}x{\left(1-x\right)}^5 dx$

Evaluate $\underset{0}{\overset{1}{\int }}{\tan }^{-1}\left(\frac{2x-1}{1+x-x^2}\right)dx$

By using properties of definite integrals, evaluate$\underset{0}{\overset{\raisebox{1ex}{$\text{π}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\int }}\frac{a sec x + b \cos ec x}{sec x + \cos ec x}dx.$