Definite Integration by Substitution

Definite Integration by Substitution

Definite Integration by Substitution requires to convert upper and lower limits of definite integration.
$$ \displaystyle \int_{x=a}^{x=b}{f(x)}dx = \int_{u=c}^{u=d}{f(u)}du
$$

Practice Questions of Definite Integration by Substitution

Question 1

Find \( \displaystyle \int_{-1}^{0}{x(1+x)^{10}}dx \).

Question 2

Find \( \displaystyle \int_{0}^{1}{x \sqrt{1-x^2}}dx \).

Question 3

Find \( \displaystyle \int_{3}^{18}{\frac{x}{\sqrt{x-2}}}dx \).