Integration Trigonometric Functions
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(1) S cos2xsin2xdx
(2) S tan2xsecxdx
(3) S sinxcosxdx using four different methods
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Solution Summary
The expert calculates the integration trigonometric functions. Sin functions are determined.
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(1)
∫cos2xsin2xdx
Use the fact that sin2x = 2sinxcosx:
∫cos2xsin2xdx = ∫cos2x(2sinxcosx)dx
Move the 2 outside the integral and combine the cosx terms:
2∫cos3xsinxdx
The derivative of cosx is -sinx, so use u substitution (u = cosx, du = -sinxdx):
-2∫u3du
Integrate:
-2(u4/4) + c
Simplify and plug cosx back in for u:
-cos4x + c
2
(2)
∫tan2xsecxdx
We know that tan2x = sec2 - 1:
∫tan2xsecxdx = ...
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