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integration by parts watch

1. Hey, got a really odd answer for this question... could someone please confirm it?! integral of (x-1)(x+1)^3 dx with limits 2->0 , integration by parts. Sorry none of the symbols work on this comp. I got -236.25 - somehow dont think that's right!! Thanks
franks xxx
2. If that was (x+1)^3 multiplied by (x-1), then the answer should be 42/5, which I did by multiplying out the brackets, but what values of u and v did you use?
Unless i misunderstood the question, it is awkward without symbols.
3. To check, you can make the integral easy by using the sub y = x+1
4. (Original post by franks)
Hey, got a really odd answer for this question... could someone please confirm it?! integral of (x-1)(x+1)^3 dx with limits 2->0 , integration by parts. Sorry none of the symbols work on this comp. I got -236.25 - somehow dont think that's right!! Thanks
franks xxx
use integration by substitution:

let u = x + 1
du/dx = 1 thus du = dx

x + 1 = u - 2

then you get

∫u³(u - 2)du, with limits 3, 1

which is just ∫u^4 -2u³ du

simple!
5. (Original post by franks)
Hey, got a really odd answer for this question... could someone please confirm it?! integral of (x-1)(x+1)^3 dx with limits 2->0 , integration by parts. Sorry none of the symbols work on this comp. I got -236.25 - somehow dont think that's right!! Thanks
franks xxx
u = (x-1), dv/dx = (x+1)³
du/dx = 1, v = ¼(x+1)4

∫(x-1)(x+1)³dx
= ¼(x-1)(x+1)4 - ¼∫(x+1)4dx
= ¼(x-1)(x+1)4 - (x+1)5/20

Definite integral between 2 and 0
= ¼(2-1)(2+1)4 - (2+1)5/20 - (¼(0-1)(0+1)4 - (0+1)5/20
= 81/4 - 243/20 + 1/4 + 1/20
= 42/5
6. maaaan Im so STUPID !!!! I just assumed that when you inserted 0 into the equation, it came to 0 - thanks so much for shoving me back in the right direction !!
franks xxx

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