We can derive reduction formula for the integration of the form ^ n x d x, ^ n x d x, ^ n…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
We can derive reduction formula for the integration of the form \(\int \sin ^{n} x d x, \int \cos ^{n} x d x, \int \tan ^{n} x d x\)and other integrals of these form using integration by parts. In turn these reduction formulas can be used to compute integrals of higher power of sin x and cos x.
If \(\int \sin ^{5} x d x=-\frac{1}{5}\)sin4x cos x + A sin2x cos x \(-\frac{8}{15}\)cos x + c then A is equal to
- \(-\frac{2}{15}\)
- \(-\frac{3}{5}\)
- \(-\frac{4}{15}\)
- \(-\frac{1}{15}\)
Answer
(C) - 4 15
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