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integrate the following integral ∫ cos mx cos nx dx , m is unequal to n

 
integrate the following integral
∫ cos mx cos nx dx , m is unequal to n

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int cos(mx)cos(nx)dx
I = \frac{1}{2}\int 2cos(mx)cos(nx)dx
I = \frac{1}{2}\int [cos(m-n)x+cos(m+n)x]dx
I = \frac{1}{2}[\int cos(m-n)xdx+\int cos(m+n)xdx]
I = \frac{1}{2}[\frac{sin(m-n)x}{m-n}+\int cos(m+n)xdx]
I = \frac{1}{2}[\frac{sin(m-n)x}{m-n}+\frac{sin(m+n)x}{m+n}]+c

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