(a) Find sin cos d. (b) You probably solved part (a) by making the substitution...
Question:
(a) Find ∫ sinθ cos θ dθ.
(b) You probably solved part (a) by making the substitution w = sin θ or w = cos θ. (If not, go back and do it that way.) Now find ∫ sin θ cos θ dθ by making the other substitution.
(c) There is yet another way of finding this integral which involves the trigonometric identities
sin(2θ) = 2 sin θ cos θ
cos(2θ) = cos2 θ − sin2 θ.
Find ∫ sinθ cos θ dθ using one of these identities and then the substitution w = 2θ.
(d) You should now have three different expressions for the indefinite integral ∫ sin θ cosθ dθ. Are they really different? Are they all correct? Explain.
Step by Step Answer:
Applied Calculus
ISBN: 9781119275565
6th Edition
Authors: Deborah Hughes Hallett, Patti Frazer Lock, Andrew M. Gleason, Daniel E. Flath, Sheldon P. Gordon, David O. Lomen, David Lovelock, William G. McCallum, Brad G. Osgood, Andrew Pasquale