JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int \frac{\cos x d x}{\sin ^{3} x\left(1+\sin ^{6} x\right)^{2 / 3}}=f(x)\left(1+\sin ^{6} x\right)^{1 / \lambda}+c\) where \(c\) is a constant of integration, then \(\lambda f\left(\frac{\pi}{3}\right)\) is equal to
- A \(-2\)
- B \(-\frac{9}{8}\)
- C \(2\)
- D \(\frac{9}{8}\)
Answer & Solution
Correct Answer
(A) \(-2\)
Step-by-step Solution
Detailed explanation
\(\int \frac{\cos x d x}{\sin ^{3} x\left(1+\sin ^{6} x\right)^{2 / 3}}\) \(=\frac{-6}{-6} \int \frac{\cos x d x}{\sin ^{7} x\left(\frac{1}{\sin ^{6} x}+1\right)^{2 / 3}}\) \(=-\frac{1}{6} \times 3\left(\frac{1}{\sin ^{6} \mathrm{x}}+1\right)^{\frac{1}{3}}+\mathrm{c}\)…
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