First slide

Introduction to definite integration

Question

If $m \neq n, m, n \in N$ then the value of $\int_{0}^{2 π} \cos m x \cos n x d x$ is

Easy

A

0
B

$2 π$
C

$π$
D

dependent on $m$ and $n$

Solution

$\begin{array}{l} \int_{0}^{2 π} \cos m x \cos n x d x \\ = \frac{1}{2} \int_{0}^{2 π} [\cos (m + n) x + \cos (m - n) x] d x \\ = \frac{1}{2} {[\frac{1}{m + n} \sin (m + n) x + \frac{1}{m - n} \sin (m - n) x]}_{0}^{2 π} \\ = 0 \end{array}$

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