Find \int \sin ^5 (\frac{x}{2}) \cdot \cos (\frac{x}{2}) \dx

CBSE Class 12 Math 2020 Outside Delhi Set 2 Solved Paper

Question : 5 of 11

Marks: +1, -0

Find

∫ sin \;^5 (\;{x}/{2}) ⋅ \cos (\;{x}/{2}) \dx

Solution:

I=∫ sin \;^5 (\;{x}/{2}) \cos (\;{x}/{2}) \dx

Putting

sin \; (\;{x}/{2}) =t

gives

I=2 ∫ t^5 \dt

∴ I=\;{t^6}/{3}+C=\;{1}/{3} sin \;^6 (\;{x}/{2}) +C

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