Not really sure what this question is asking. I know how to find integral and everything, but I'm not sure what the instructions mean.

express the definite integral in terms of u but do not evaluate:

integral from 0 to 3 of -8x/((2x^2 + 2)^2)

Then I am given u to be 2x^2 + 2

Question

Not really sure what this question is asking. I know how to find integral and everything, but I'm not sure what the instructions mean.


express the definite integral in terms of u but do not evaluate:

integral from 0 to 3 of -8x/((2x^2 + 2)^2)

Then I am given u to be 2x^2 + 2

phi · Answer

I would start by find du in terms of x

anonymous · Answer

Okay du = 4xdx

phi · Answer

now start replacing terms in the original with u and du

anonymous · Answer

So -2 u^-2 du right

phi · Answer

looks good

anonymous · Answer

Is that as far as they want me to take it do you think?

phi · Answer

the final step is to redo the bounds
u = 2x^2 + 2

replace x with0 and 3 to find the bounds for u

anonymous · Answer

Ah right adjusting the limits. So lower limit is now 2 and upper is 20

phi · Answer

yes
$$ \int_2^{20} -2 u^{-2} \ du $$

anonymous · Answer

Alright Thank you so much!