Allied & ICAR Exam Bank • ALLIED_0033 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The value of $\int_0^{\pi/2} \sin^3(x) \cos(x) dx$ is:

Answer Key:

0.25

Step-by-Step Solution & Explanation

Let $u = \sin x \implies du = \cos x dx$. The integral becomes $\int_0^1 u^3 du = \left[ \frac{u^4}{4} \right]_0^1 = 0.25$.
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