Question

If f(3)=13, f' is continuous, and the integral from 3 to 5 f'(x)dx=24 then the value of f(5) is ?

Answer 1

Since

∀x,f'(x)=f'(x) , f is a primitive function of

f'

.Therefore,

∫

5

3

f

'

(

x

)

d

x

=

f(x)

:∣53=f(5)−f(3)

f(5)−13=24

by the fundamental theorem of calculus(part 2) (because

f'

is continuous and thus integrable).

Thus,

f(5)=24+13=37 .

Answer 2

this is the solution of this question