TS EAMCET · Maths · Indefinite Integration
If \(\int \sin (101 x)(\sin x)^{99} d x=\frac{\sin (100 x)(\sin x)^\lambda}{\mu}+\mathrm{c}\) then \(\frac{\lambda}{\mu}=\)
- A \(1\)
- B \(2\)
- C \(4\)
- D \(8\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \int \sin (101 x) \cdot(\sin x)^{99} d x \\ & =\int \sin (100 x+x) \cdot(\sin x)^{99} d x \\ & =\int(\sin 100 x \cdot \cos x+\cos 100 x \cdot \sin x)(\sin x)^{99} d x \\ & =\iint_{\text {I }} \sin (100 x) \cdot \underbrace{\cos x \cdot(\sin x)^{99}}_{\text {II…
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