CBSE Class 12 Math 2020 Outside Delhi Set 2 Solved Paper

Question : 5 of 11

Marks: +1, -0

Find

\int \sin^5\left(\frac{x}{2}\right) \cdot \cos\left(\frac{x}{2}\right) \, dx

Solution: 👈: Video Solution

I = \int \sin^5\left(\frac{x}{2}\right) \cos\left(\frac{x}{2}\right) \, dx

Putting

\sin\left(\frac{x}{2}\right) = t

gives

I = 2 \int t^5 \, dt

\therefore I = \frac{t^6}{3} + C = \frac{1}{3} \sin^6\left(\frac{x}{2}\right) + C

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