Write an expression for the function, f(x), if it is known that f '(x) = cos(x2) and f(4) = 5. Give your answer using the form below.

Question

anonymous · Answer

$$f(x)=\int\limits_{a}^{x}A(t)dt$$

bahrom7893 · Answer

ok this is just integration. What's the integral of $$Cos(x^2)$$?

anonymous · Answer

Oh, sorry, it's f(x) = C plus the integral.

anonymous · Answer

sin(x^2)*(1/2)

anonymous · Answer

I know C=5 and A(t)=cos(t^2)
But I'm having trouble finding little a to put on the bounds on the integral.

bahrom7893 · Answer

Oh you need to put the bounds first?

anonymous · Answer

Yeah, you have to determine what C, a, and A(t) are. So I got that C was 5 and that A(t)=cos(t^2) due to the second fundamental theorem. But I'm stuck with finding the lower bound.

anonymous · Answer

$$f(x)=5+\int\limits_{a}^{x}\cos(t^{2})dt$$

bahrom7893 · Answer

hang on let me pull up my notes on this. It's been a while.

anonymous · Answer

Okay.

bahrom7893 · Answer

Wait why do you need the limits again?

bahrom7893 · Answer

You don't need to know the limits, just integrate by parts:
u = Cos(x^2)
dv = dx

anonymous · Answer

Okay. Thank you!