\(\int\limits_0^\pi \sin ^3 x \cdot \cos

CUET Preparation Today

Start Free Mocks

Home Questions YZY5TNGKYU

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Definite Integration

Question:

$\int\limits_0^\pi \sin ^3 x \cdot \cos ^2 x \cdot d x = $

Options:

$\frac{-4}{15}$

$\frac{2}{15}$

$\frac{4}{15}$

Correct Answer:

$\frac{4}{15}$

Explanation:

$I=2\int\limits_0^{\pi/2} \sin ^3 x × \cos ^2 x dx $

By applying $\int\limits_a^b+(x)dx=\int\limits_a^bf(a+b-x)dx....$

$=\frac{2×(3-1)(3-2)(2-1)}{5×3×1}=\frac{4}{15}$

Option 4 is correct.