SATHEE: Definite Integration Question 38

Definite Integration Question 38

Question 38

For any integer $n$ , the integral $\int_{0}^{π} e^{\cos^{2} x} \cos^{3} (2 n + 1) x d x$ has the value

(1985, 2M) (a) $π$ (b) 1 (c) 0 (d) None of these

Show Answer

Solution:

Let $I = \int_{0}^{π} e^{\cos^{2} x} \cdot \cos^{3} (2 n + 1) x d x$

$0, f (a - x) = - f (x)$

Again, let $f (x) = e^{\cos^{2} x} \cdot \cos^{3} (2 n + 1) x$

$Missing or unrecognized delimiter for \left$

$∴ I = 0$

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