I need help figuring out this problem!

Write an expression for the function f(x) if it is known that f'(x)=cos(x^2) and f(1)=7

f(x)=C+integral from a to x A(t)dt

C=
a=
A(t)= cos(t^2)

Question

I need help figuring out this problem!

Write an expression for the function f(x) if it is known that f'(x)=cos(x^2) and f(1)=7

f(x)=C+integral from a to x A(t)dt

C=
a=
A(t)= cos(t^2)

anonymous · Answer

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

ganeshie8 · Answer

use FTC

abb0t · Answer

@Squirrels

ganeshie8 · Answer

$$\large f(x) - f(a) =   \int \limits_a^x  f'(t) dr$$

ganeshie8 · Answer

plugin $a = 1$  and the given function $f'(x) $

ganeshie8 · Answer

$$\large f(x) - f(1) =   \int \limits_1^x  \cos (t^2) dt$$

$$\large f(x)  =  f(1) +    \int \limits_1^x  \cos (t^2) dt$$

$$\large f(x)  =   7 +    \int \limits_1^x  \cos (t^2) dt$$