Question

Evaluate the integral

Answer 1

\[\int\limits_{1}^{2} (4 + u ^{2})/u ^{3}\]

Answer 2

This one is simple, just separate and integrate.

Answer 3

Ok, first of all devide 4 and u^2 by u^3... Then we will got integral from 1 to 2 = 4/u^3 + 1/u. Then, Integrate both numbers and then just do the highschool math.. ;)

Answer 4

I would try u substitution and have u=u^3

Answer 5

\[(4/u^{3}) + 1/u ==> 4u/(2)u^{2} +\ln(u)\]

Answer 6

nope, integral of 4/u^3 is equal to -2/u^2 + C

Answer 7

ahh yes forgot my - but other than that i am close

Answer 8

Ofcourse, then you will finish this integral by putting 2 and 1 to the integral.

Answer 9

see all of that is fine and dandy but I plug in the numbers and i get( -1+ln(2) )- ( (-1/2)+0 )

Answer 10

and the answer is (3/2)+ln(2) so my signs are wrong?

Answer 11

Yes, you should have got this -> (-2 + ln(2) ) - ( -2 + 0 ) = ln (2)

Answer 12

according to this the (3/2)+ln(2) is correct, my answer would have been (1/2)+ln(2)