WBJEE · Maths · Definite Integration
The value of the integral \(\int_0^{\pi / 2} \sin ^5 x d x\) is
- A \(\frac{4}{15}\)
- B \(\frac{8}{5}\)
- C \(\frac{8}{15}\)
- D \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{8}{15}\)
Step-by-step Solution
Detailed explanation
Hints : \(I=\int_0^{\frac{\pi}{2}} \sin ^4 \mathrm{x} d \mathrm{dx} \quad \cos \mathrm{x}=\mathrm{f}, \sin \mathrm{d} \mathrm{x}=\mathrm{dt}\) \(=-\int_1^0\left(1-t^2\right) d t=\int_0^2\left(t^4-2 t^2+1\right) d t\)…
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