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

Find the integration of $x^2+3x.$

Find the value of $\int 5\sin xdx.$

Evaluate ${\int }_0^{\frac{\mathrm{\pi }}{2}}\frac{\left(1-{\sin }^{2}x\right)\left(4\sin x-3\right)}{\left(4-{\cos }^{2}x\right)\left(\sin x+4\right)\cos x}dx.$

Find the integral of $\int -u^p{e}^{-u}du.$

Let $f\left(x\right)=\left|x-2\right|, g\left(x\right)=x^2-5 \text{and} h\left(x\right)=x^3$. Then ${\int }_2^{4}g\left(x\right)dx+{\int }_1^{2}4h\left(x\right)dx=$

Let $f\left(x\right)=\left|x-2\right|, g\left(x\right)=x^2-5 \text{and} h\left(x\right)=x^3$. Then ${\int }_1^4\left(\frac{g\left(x\right)}{h\left(x\right)}\right)dx=$

Let $f\left(x\right)=\left|x-2\right|, g\left(x\right)=x^2-5 \text{and} h\left(x\right)=x^3$. Then ${\int }_0^{3}f\left(x\right)dx+{\int }_2^{3}h\left(x\right)dx=$

The value of the integral ${\int }_0^{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\log \left[\sin \right(\mathrm{x}\left)\right]\mathrm{dx}$ is