Question

evaluate using the fundamental theorem of calc

Answer 1

You mean
\[\int_1^9 \sqrt{x}~dx\]
right?

Answer 2

yes!

Answer 3

\[\sqrt{x}=x^{1/2}\]
You can then use the power rule directly:
\[\int x^{1/2}~dx=\frac{x^{3/2}}{\frac{3}{2}}+C=\frac{2}{3}x^{3/2}+C\]
Then just work through that like you would with any other definite integral.

Answer 4

how do you sue the pwoer rule

Answer 5

\[\int x^n~dx=\frac{x^{n+1}}{n+1}+C\]

Answer 6

In this case \(n=\dfrac{1}{2}\)