# Thread: Fundamental Theorem of Calculus

1. ## Fundamental Theorem of Calculus

if f(x) = \int from 0 to x of (x^2)*(sin(t^2)) dt, find f'(x)

i wanna believe that it is just (x^2)*(sin(x^2)) but it seems like that is too simple of an answer since I'm doing this in the problems plus section of chapter five.

2. Originally Posted by CalculusABStudent
if f(x) = \int from 0 to x of (x^2)*(sin(t^2)) dt, find f'(x)

i wanna believe that it is just (x^2)*(sin(x^2)) but it seems like that is too simple of an answer since I'm doing this in the problems plus section of chapter five.
Assuming the x^2 is NOT a typo, then you can re-write the function as $f(x) = x^2 \int_0^x \sin(t^2) \, dt$. Now use the product rule.

If it IS a typo, then the obvious answer is correct.

3. not a typo.
and thankyou!

4. x^2 (sin⁡(x^2 ) )+∫_0^x▒〖sin⁡(t^2 )dt〗(2x)