TS EAMCET · Maths · Definite Integration
\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x=\)
- A \(\frac{2}{3}\)
- B \(\frac{3}{10}\)
- C \(\frac{4}{15}\)
- D \(\frac{5}{18}\)
Answer & Solution
Correct Answer
(C) \(\frac{4}{15}\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x\)...(i) Using \(\int_a^b f(x)=\int_a^b f(a+b-x)\) \(I=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin ^2 x \cos ^2 x(-\sin x+\cos x) d x\)...(ii)…
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