AP EAMCET · Maths · Indefinite Integration
Find the value of \(k\) if \(\int \cos ^k(x) \sin (x) d x=\frac{-1}{4}\) \(\cos ^4(x)+c\)
- A \(4\)
- B \(3\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
To find \(k\) Given, \(\int \cos ^k(x) \sin (x) d x=\frac{-1}{4} \cos ^4(x)+C\) Let \(I=\int \cos ^k(x) \sin (x) d x\) Let \(\cos x=t\) \(\Rightarrow \quad-\sin x d x=d t\) \(\sin x d x=-d t\) \(\therefore \quad I=-\int t^k d t\)…
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