Definite integration by parts Problems and solutions

The integration by parts is a mathematical approach, used to evaluate the definite integrals of the product of two or more functions. The worksheet on the integration by parts rule is a list of example questions on definite integrals for practice and also solutions to learn how to use the integration by parts in finding the definite integrals of the product of the functions in definite integral calculus.

Evaluate $\displaystyle \int_{0}^{\Large \frac{\pi}{2}}{x\cos{x}}\,dx$

Evaluate $\displaystyle \int_{0}^{1}{e^{\displaystyle x^2}.x^3}\,dx$

Evaluate $\displaystyle \int_{0}^{\Large \frac{\pi}{4}}{x\sec^2{x}}\,dx$

Evaluate $\displaystyle \int_{0}^{\Large \frac{\pi}{2}}{x\sin{x}}\,dx$