Question

what is the integral of sqrt(x-1)??

Answer 1

well, what's this integral:
\[ \int x^{1/2} \ dx \]
?

Answer 2

In general, if \( n \neq -1 \),
\[ \int x^n \ dx = \frac{1}{n+1} x^{n+1} + C \]

Answer 3

So what's the integral I just wrote down?

Answer 4

Once you know that, use a change of variables, \( u = x - 1 \) and you have the answer to your problem.

Following?

Answer 5

u = x-1
du = dx
now you have the integral of u^(1/2) du
This gives you 2/3*u^(3/2)
Plugging (x-1) back in for u gives you a final solution of:
(2/3)*(x-1)^3/2

Answer 6

+ C after that answer... don't forget that haha