I have a question about line integrals. I'm getting a different answer than WolframAlpha, though it is pretty darn close when it comes to the step by step solution. I'm going to assume my algebra is wrong but am not sure where. Attached photos are my work and Wolfram Alphas answer. If someone could take a look at it that would be awesome.

Question

anonymous · Answer

Here is the work.

amistre64 · Answer

you dont need a +C

amistre64 · Answer

$$\int_{1/2}^{1}t(16t^2+9)^{1/2}~dt$$
$$u=16t^2+9~:~u=[13,25]\~\\frac{du}{32t}=dt$$
$$\frac{1}{32}\int_{13}^{25}(u)^{1/2}~du$$
$$\frac{1}{32}\frac{3}{2}(25^{2/3}-13^{2/3})$$

amistre64 · Answer

dbl chk that since i am prone to some error at times :)

anonymous · Answer

Thank you. That makes sense.

amistre64 · Answer

http://www.wolframalpha.com/input/?i=integrate+%28u%5E%281%2F2%29%2F32%29+du%2C+from+13+to+25 its coming out the same on the wolf :)

anonymous · Answer

I always double check. Need to be able to for one replicate the results and two I need the answer to be correct. Thanks again.

amistre64 · Answer

youre welcome ;)