SOLUTION: Hi all, can somebody please help me with the following? I have to evaluate the following intergral using the given substitution.
∫e^-(sin x)cos x dx, substitution u = sinx
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Question 216792: Hi all, can somebody please help me with the following? I have to evaluate the following intergral using the given substitution.
∫e^-(sin x)cos x dx, substitution u = sinx
Any help would be great.
Thanks, -Nick.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Since we are given the substitution to use the solution is pretty straightforward. Start with:
u = sin(x)
Express the derivative of each side:
du/dx = cos(x)
Multiply both sides by dx:
du = cos(x)*dx
We can see the right side of the last equation in our integral. We can also see the right side of u = sin(x) in the integral. So we can substitute for both of these giving:
In this form the integral is easy to find:
=
And finally we substitute back sin(x) for u:
=
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