Question

Which method evaluates the definite integral below?

$$\int_{0}^{3}2x(x^2+2)^{3}\,dx$$

Accepted Answer

$$\begin{aligned}&	ext{set }u=x^{2}+2	ext{,}\ &	ext{change bounds from }x\in[0,3]	ext{ to }u\in[2,11]\end{aligned}$$

Answer

$$\begin{aligned}&	ext{set }u=x^{2}+2	ext{,}\ &	ext{change bounds to }u\in[11,2]\end{aligned}$$

Answer

$$\begin{aligned}&	ext{set }u=2x	ext{,}\ &	ext{then keep the original bounds in the }u	ext{ integral}\end{aligned}$$

Answer

$$\begin{aligned}&	ext{set }u=x^{2}+2	ext{,}\ &	ext{keep }x\in[0,3]	ext{ as the }u	ext{ bounds}\end{aligned}$$

Practice: Integration - Definite Substitution Method