Consider the integral x^ 3 1 - x^ 4 ,dx

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

Problem

Consider the integral

\int x^{3}\sqrt{1 - x^{4}}\,dx.

Which substitution will MOST directly transform the integrand into a simple power of the new variable that can be integrated in a single step? (a)

u = x^{4}

(b)

u = 1 - x^{2}

(c)

u = 1 - x^{4}

(d)

u = \sqrt{1 - x^{4}}