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)

Answer 1

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

Answer 2

use FTC

Answer 3

@Squirrels

Answer 4

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

Answer 5

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

Answer 6

\[\large f(x) - f(1) = \int \limits_1^x \cos (t^2) dt\]

\[\large f(x) = f(1) + \int \limits_1^x \cos (t^2) dt\]

\[\large f(x) = 7 + \int \limits_1^x \cos (t^2) dt\]