Question

Use the Fundamental Theorem of Calculus to determine the answer to the problem; do not use the even/odd properties of integration.

Answer 1

56665

Answer 2

Problem is: \[\int\limits_{-\frac{ \pi }{ 2 }}^{\frac{ \pi }{ 2 }}(\sin^3x \cos x+\sin x \cos x)dx\]

Answer 3

\[\sin ^{2} x is meant (\sin(x))^{2}\]
so you are using quotient rule for sin square. and cos x anti-derivative was sin x

Answer 4

Then plug pi/2 and - pi/2 in the equation

Answer 5

Then take the number when you plug pi/2 subtract the number when you plug -pi/2 and get the answer

Answer 6

Hope this help

Answer 7

@MoonlitFate find the integral using u substitution (see attachment)

Answer 8

then evaluate the integral from b to a (see attachment 2)

verification of answer @ http://www.wolframalpha.com/input/?i=integral+of+sin^3xcosx%2Bsinxcosx+from+-pi%2F2+to+pi%2F2