What are F(1) and F'(1) for F(x) = \int_{-x}^{x} \frac{dt}{1+t^2}?

[ziddy83]

Ok i have another problemo here...

if $$F(x) = \int_{-x}^{x} \frac{dt}{1+t^2}$$

Find F(1) and F'(1)...I need some assistance...the anti derivative is

$$arctan(t)$$ so then... do i set that equal to f(1) and solve for t? and then for F', take the derivative and then solve for t again? I am kind of confused...

 

[OlderDan]

Ok i have another problemo here...

if $$F(x) = \int_{-x}^{x} \frac{dt}{1+t^2}$$

Find F(1) and F'(1)...I need some assistance...the anti derivative is

$$arctan(t)$$ so then... do i set that equal to f(1) and solve for t? and then for F', take the derivative and then solve for t again? I am kind of confused...

You can do the integral to get F(x) for all x in the domain of F. Then take the derivative with respect to x to get F'(x). Evaluate both at x = 1. You can also find F'(x) using the fundamental theorem of calculus. For the latter approach, you might want the break the integral into two intervals at any constant a such that -x<a<x. a = 0 would be a convenient choice, but any constant value will do.

 

[ziddy83]

ok i got it ..thank you.