Evaluate the definite integral. (The answer should be 16/15.)?

Question

The integral (with upper limit 2 and lower limit 1) of x * sqrt(x-1) dx.
Please show your work. Thank you for your help.

Answer 1

Let u = x-1. The limits change to upper 1 and lower 0; dx = du; and the integral becomes (u+1)sqrt(u), or u^1.5 + u^0.5.

Integrating that gives 2/5 u^2.5 + 2/3 u^1.5. Substitute in u = 1 and u = 0 to get (2/5 + 2/3) - (0+0) = 16/15.

Answer 2

OK, here, you want someone to do your homework for you and you come on Yahoo Answers casue ya know the smartest people dwell here.

So, yeah, let me see......Integral, you say? Yep, I know the answer is 16/15...you didn't have to tell me that. Let's see, take the 3 from the 6, times a 2 (I like 2's), something crap about a pie (Don't know what pie has to do with math but seems math people like pie, go figure) so, ah, yeah back to the question......dot the i, cross my t and Ok, yeah, you're right the answer IS 16/15!

Man, thank god for those catholic school nuns! I am Smart, huh?

Answer 3

substitution will work best
u=x-1 du=dx
x=u+1

so now the integral is:
(u+1)Sqrt[u]du=
(u^(3/2)+u^(1/2))du=
(2/5)u^(5/2) + (2/3)u^(3/2)
the limits are now 1 and 0 since 2-1=1 and 1-1-0

(2/5)(1)+(2/3)(1)-0-0=
2/5+2/3=
6/15+10/15=
16/15