Expert: Frederick Koh - 2/8/2012

Question
Hi,

I need to find the definite integral on the interval (0,5) of |3(x^2)-8(x)|. I divided it into the negative and positive intervals and tried to find the integral of -(3(x^2)-8(x)) on (0,8/3) and (3(x^2)-8(x)) (8/3,5). The first set came out to zero and the second came out to 25 when I did it yet I know the answer should be 49.6. What am I doing wrong?

Thanks,
Zach Rose

Answer
Firstly, your final answer should be 43.96, not 49.6 (I have verified this using a graphic calculator)

Secondly, if the first integral of -(3(x^2)-8(x)) on (0,8/3) gives you zero, most likely you have substituted the limits right away without doing the integration, because [-(3(8/3)^2-8(8/3))- 0 ] =0

Thirdly, you will have to recalculate your two integrals once again; the cleaving of the integrals into the two intervals is perfectly correct though.

integral of -(3(x^2)-8(x)) on (0,8/3) should give 9.48

and integral of (3(x^2)-8(x)) (8/3,5) should give 34.48

Adding the two gives 43.96.

Hope this helps. Peace.