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 \(\int \operatorname{cosec}^{n} x d x=-\frac{\operatorname{cosec}^{n-2} x \cot x}{n-1}+A \int \operatorname{cosec}^{n-2} x d x\)
then A is equal to
- \(\frac{1}{n-2}\)
- \(\frac{n}{n-2}\)
- \(\frac{n-1}{n-2}\)
- \(\frac{n-2}{n-1}\)
Answer
(D) n-2 n-1
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