A definite integral is to be evaluated by making the substitution

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

A definite integral

\displaystyle\int_{0}^{2} x^{3}(x^{4}+1)^{5}\,dx

is to be evaluated by making the substitution

u=x^{4}+1

. Which of the following gives the correct new limits of integration expressed in terms of

u

? (a)

u

goes from

0

2

(b)

u

goes from

1

16

(c)

u

goes from

1

17

(d)

u

goes from

0

16