find the indefinite integral of the trigonometric function:
1. integral cos theta/ sin theta dtheta
2. integral tan 5 theta dtheta
3. integral csc 2x dx
thanks!!
2007-03-28 13:25:45 · 2 answers · asked by oceanblue879 1 in Science & Mathematics ➔ Mathematics
The first question, cos theta over sin theta d-thetais the same as the integral of tantheta d-theta, which is equal to the natural log (ln) of the absolute value of sec theta plus C.
The second question is a u-sub equation, where u is equal to 5 theta, and du is equal to 5 d-theta. So you multiply the integral by 1/5 to account for the 5 in the u-sub, and get tan(u)du, which is the answer to number one. Then you sub 5 theta in for u, and the answer comes out to be 1/5 times ln of the absolute value of sec theta plus C.
The final question is again a u-sub where u=2x. du=2dx, so mulitply the integral by 1/2 to account for the 2, and integrate cscu to get the answer which is 1/2 times the natural log of the absolute value of 1/2 times u plus C.
2007-03-28 13:45:52 · answer #1 · answered by Lockedbox 2 · 0⤊ 0⤋
1) ln sin(theta) +c
2) ln sin(5 theta)*1/5 +c
3) 1/2ln tan 2x +c
2007-03-28 13:34:41 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋