For finding the area bounded by y=sinx, y=x, and x=pi/4 i took the integral of (x-sinx)dx from 0 to pi/4 got x^2/2+cosx but im not getting the right answer when i plug in pi/4. (the right answer should be 0.0155 units^2) is there an error in my integration that still evades me or is it a bigger error?

Question

For finding the area bounded by y=sinx, y=x, and x=pi/4 i took the integral of (x-sinx)dx from 0 to pi/4 got x^2/2+cosx but im not getting the right answer when i plug in pi/4.  (the right answer should be 0.0155 units^2) is there an error in my integration that still evades me or is it a bigger error?

anonymous · Answer

you made a mistake when you wrote x - sin(x) dx.

DRAW THE GRAPH FIRST! when you do these kind of questions. I cannot believe how many times I have messed these types of questions up on the test. DRAW THE DAMN THING!

even if you draw it roughly you will get the correct answer.

anonymous · Answer

I graphed it on my calculator.  so (sinx-x)dx?

anonymous · Answer

are you sure your answer is right?

try this ...

x^2/2 + cos(x) -->   (0 + cos(0))   -   (pi^2/32) + cos(pi/4)

1 - (pi^2/32) - 1/sqrt(2)  = right answer?

anonymous · Answer

nono x - sin(x) is correct.

anonymous · Answer

sorry take the negative of my answer

-1 + (pi^2/32) + 1/sqrt(2)

anonymous · Answer

ok, thanks.

anonymous · Answer

that should be right. if it not right then the multiple choice you are given has no correct answers