Question

How would I find the value of a function at a certain point given the intergral?

Answer 1

I'll type the actual problem out here.

Answer 2

\[F(x)=\int\limits_{0}^{x}dt \div(t^2+9)\]

Answer 3

WHat would F(2) be?

Answer 4

you need to solve for integral and then plug in x = 2.

\[F'(t) = \frac{ 1 }{ t^2 + 9 }\]

F(t) is the integral of F'(t) and plugging in 0 to x by FTC turn it into F(x)

plug in 2 after ^_^

Answer 5

Does it matter that in my problem it has F(x)= rather than F(t)=?

Answer 6

not at all since it is the integral from 0 to x

Answer 7

by FTC:

\[F(x) = \int\limits_{0}^{x}f'(t) dt\]

Answer 8

Oh! right, that makes total sense. Thank you!

Answer 9

And If I wanted to find the derivative I just plug in x for t right?

Answer 10

not sure the derivative of which function you mean

Answer 11

the derivative of the intergral.

Answer 12

F'(x) in this case.

Answer 13

for some reason i'm not understanding the question. sorry ^_^