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

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

Grade:12

1 Answers

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

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

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