AP EAMCET · Maths · Definite Integration
If \(u(n)=\int_0^{\frac{\pi}{2}}(1+\sin t)^n \sin 2 t d t, n \in N\), then \(u(4)=\)
- A \(\frac{28 \pi}{5}\)
- B \(\frac{128}{35}\)
- C \(\frac{129}{15}\)
- D \(\frac{68 \pi}{15}\)
Answer & Solution
Correct Answer
(C) \(\frac{129}{15}\)
Step-by-step Solution
Detailed explanation
Given \(u(n)=\int_0^{\pi / 2}(1+\sin t)^n \sin 2 t d t\) \(\Rightarrow \mathrm{u}(\mathrm{n})=2 \int_0^{\pi / 2}(1+\sin \mathrm{t})^{\mathrm{n}} \sin \mathrm{t} \cos \mathrm{t} d \mathrm{t}\) Let \(1+\sin \mathrm{t}=\mathrm{u} \Rightarrow \cos \mathrm{tdt}=\mathrm{du}\)…
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