\(\int\limits_0^\pi \sin ^3 x \cdot \cos ^2 x \cdot d x = \)
Answer & explanation
Correct answer: option 4
\(I=2\int\limits_0^{\pi/2} \sin ^3 x × \cos ^2 x dx \)
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.