Question

how to evaluate an integral.

Answer 1

\[\int\limits_{-1}^{-8}((x-x^2)/(2(x^(1/3)))dx\]

Answer 2

i know the derivative is (-3/80)x^(5/3)(5x-8)
but how do i evaluate it with the given intervals.

Answer 3

After you integrate it, let say you get f(x).
Then, you will do f(-8) - f(-1)

Answer 4

\[(-3/80)x ^{5/3}(5x-8)\]

Answer 5

you mean the mean value theorem>?

Answer 6

and c would be the answer?

Answer 7

Hmm.......
Let f(x) = \(−\frac{3}{80}x^\frac{5}{3} \ (5x−8)\)
(1) Evaluate f(x) at x = -8 (Upper limit)
(2) Evaluate f(x) at x =-1 (Lower limit)

Then do (1) - (2)

Answer 8

i get it.

Answer 9

Also, this is the second part of the Fundamental Theorem of Calculus.

Answer 10

ah, whats the first part?

Answer 11

(Second part)\[\int_a^bf(x)dx=F(b)-F(a)\]

For the first part, please visit:
http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus#First_part