Question

Evaluate \[ \int_{0}^{2}x^{3}(4-x^{2})^{\frac52}\,dx \]

• A. \(\dfrac{256}{63}\)
• B. \(\dfrac{2048}{63}\)
• C. \(\dfrac{512}{63}\)
• D. \(\dfrac{1024}{63}\)

Hint:

For integrals involving \[ x^{m}(a-x^{2})^{n}, \] use the substitution \[ \boxed{u=a-x^{2}.} \] This converts the integral into a polynomial in \(u\), making it easy to evaluate.

Answer 1

The Correct Option is D