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# integration question - FP3 watch

1. I don't get the right answer when i do this, and i cant think which bit i am doing wrong.

a curve has equation y=x^2 arsinhx

the region R is bounded by the curve the x-axis and the line x=3.

show that the area of R is 9ln(3+sqrt(10)) - 1/9 (2+7sqrt(10))

so i integrate by parts, and then use a change of variable to find the second bit. and i thought it was all going pretty well...
but I got 6ln(3+sqrt(10)) - 2sqrt(10) + 2 (which isnt right)

any help much much appreciated. xx thanks
2. How have you done the integration by parts?

If , then we want to get rid of that pesky log (in the arcsinh), so choose

and then .

Did you get that, and if you didn't, now can you do it?
yeah, i had that... i think

ive got:
[2xarsinhx - integral(2x/sqrt(x^2+1))]

so the first bit is easy, and the second bit is of the form (f '(x)[f(x)]^n), so thats easy to ingrate too.

am i on the right track?? im not sure which bit im getting wrong...

cheers
4. (Original post by rachel123456)
yeah, i had that... i think

ive got:
[2xarsinhx - integral(2x/sqrt(x^2+1))]

so the first bit is easy, and the second bit is of the form (f '(x)[f(x)]^n), so thats easy to ingrate too.

am i on the right track?? im not sure which bit im getting wrong...

cheers
If then what is v? I think that you have , so you've differentiated where you should have integrated. Try again and see if that works.
5. ooh!!! thanks very much.
i knew i was doing something stupid. - its worked a charm. cheers!!

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