114 Part I: The Questions
What to Watch Out For
You can get tripped up in a lot of little places on these problems, but hopefully these
tips will help:
✓ Not all of the trigonometric integrals fit into a nice mold. Try identities,
u-substitutions, and simplifying the integral if you get stuck.
✓ You may have to use trigonometry and right triangles in the trigonometric
substitution problems to recover the original variable.
✓ If you’ve forgotten how to do polynomial long division, you can find some
examples in Chapter 1’s algebra review.
✓ The trigonometric substitution problems turn into trigonometric integral
problems, so make sure you can solve a variety of the latter problems!
Trigonometric Integrals
884–913 Find the antiderivative or evaluate the
definite integral.
884.
sin
2
0
3 2
2θ θ
π
( )
∫
d
885.
cos
2
0
4
θ θ
π
d
∫
886. tan
2 x dx
∫
887. sec
4 t dt
∫
888. sin
sin
3
2
x
x dx
( ) ( )
∫
889. cos
cos
5
2
x
x dx
( ) ( )
∫
890. sin cos
4 x
xdx
∫
891. tan sec
2
2
x
xdx
∫
892. sin
cos
5
4
x
x dx
( ) ( )
∫