Posted by Paul on Friday, August 10, 2012 at 2:02pm.
Evaluate the following definite integral:
integral at a = 1, b=2
4dx/(9x^2+30x+25)
Would I have to separate them in 3 terms as:
4 ∫1/9x^2 + ∫1/30x + ∫1/25
resulting in: 4/(3x^3)+ (15x^2)+ C?
and from there I can replace a and b
f(a)  f(b)?
Thank you

Calculus  Steve, Friday, August 10, 2012 at 4:27pm
Booo!
1/(a+b+c) is NOT 1/a + 1/b + 1/c
What you need to do is let
u = 3x+5 and you have
du = 3 dx, so dx = du/3
x in [1,2] means u in [2,11]
giving you
∫[2,11] 4/u^2 du/3
4/3 ∫[2,11] u^2 du
That should be ever so simple.

Calculus  Paul, Friday, August 10, 2012 at 6:23pm
THanks Steve, but why 3x+5??

Calculus  Steve, Saturday, August 11, 2012 at 5:54am
because you have 9x^2 + 30x + 25 = (3x+5)^2
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