Thread: Check answer for this difinate integral

1. Check answer for this difinate integral

Hi,

Could someone please check the answer for this?
I keep coming up with an answer of 32/225. However the answer sheet has it as 16/225.

The question is evaluate the integral of 4/(1+2t)^3 on the interval of [1,2]

2. Originally Posted by Craka
Hi,

Could someone please check the answer for this?
I keep coming up with an answer of 32/225. However the answer sheet has it as 16/225.

The question is evaluate the integral of 4/(1+2t)^3 on the interval of [1,2]
$\int_1^{2}\frac{4}{(1+2t)}dt=2\int_1^{2}\frac{2}{( 1+2t)^3}=2\bigg[\frac{-1}{2(1+2t)^2}\bigg]\bigg|_1^{2}=\frac{16}{225}$

3. Do you pull the 2 out to the front of the integral due to it being a derivative of 1+2t and also a factor of the numerator?

4. Originally Posted by Craka
Do you pull the 2 out to the front of the integral due to it being a derivative of 1+2t and also a factor of the numerator?
Yes, I pulled the 2 our solely to accentuate the derivative of the quantity 1+2t being in the numerator, it is not neccasary