Question

If the function f has a continuous derivative on [0,c], then from 0 to c, integral f'(x) dx=?

Answer 1

Answer:

$\int\limits^0_c f'(x) dx =f(c)-f(0)$

Step-by-step explanation:

we are given

f has a continuous derivative on [0,c]

and we know that

derivative and integral are inverse of each other

so, we can write as

$\int \:f'\left(x\right)dx=f\left(x\right)$

we are given bound

so, we can use fundamental theorem of calculus

$\int\limits^a_b f'(x) dx =f(b)-f(a)$

we have bound from 0 to c

so, we get

$\int\limits^0_c f'(x) dx =f(c)-f(0)$