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Integral Calculus> integrate the following integral ∫ sin mx...

question mark

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

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 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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