Definite Integration of Power Functions


$$\displaystyle \int_{n}^{m}{(ax+b)^k}dx = \dfrac{1}{a(k+1)}\Big[(ax+b)^{k+1}\Big]_{n}^{m}+c$$

Example 1

Find $\displaystyle \int_{0}^{1}{(2x+1)^5}dx$.

Example 2

Find $\displaystyle \int_{0}^{1}{\dfrac{1}{(3x-2)^4}}dx$.

Example 3

Find $\displaystyle \int_{0}^{1}{\sqrt{4x+3}}dx$.






Your email address will not be published. Required fields are marked *