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8.2: Trig Integrals
By now, you should be able to integrate the basic trig functions and know the appropriate identities
for integrating the squares of the trig functions. To integrate higher powers of trig functions, the key
is, if possible, to “save” a derivative du of a trig function u and rewrite the rest of the integral in terms
of u.
Examples:
ˆ
sin3 x dx =
ˆ
π/4
tan3 x sec5 x dx =
0
Key Identities to Compute Product-to-Sum Integrals:
sin(A ± B) =
cos(A ± B) =
These are extremely important in the study of Partial Differential Equations.
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Example:
ˆ
π
sin(3x) cos(5x) dx
Compute
−π
On Beyond Average:
ˆ
cos4 x dx =
ˆ
(For your amusement...)
sec3 x dx =
2