Earlier today i was asked what i thought was going to be a simple problem and i can't for the life of me get an answer. I was asked to come up with an equation for a curve that looks like -cos(theta) from 0 - PI, has a y-intercept of 10,000, and has an area underneath of 200,000. So I immediately think -x cos(theta) + 10001 where x is the amplitude scale factor. So shouldn't I be able to set the definite integral of this equation (from 0 - PI), equal to 200000 and solve for x? Once I wrote it out I saw the problem I was going to have evaluating sin(0) and sin(PI).
[int from 0-PI] (-xcos(theta) + 10001) dtheta = 200000
-x [int from 0-PI](cos(theta) dtheta) + [int from 0-PI](10001 dtheta) = 200000
-x [sin(PI) - sin(0)] + 10001(PI) = 200000
-x(0) + 10001(PI) = 200000
10001(PI) = 200000 ?????
What am I doing wrong because all I'm getting is 10001(PI) = 200000 because my x get's multiplied by the zero sin(PI) - sin(0) leave behind. Have i set this up entirely wrong?
thanks for any help