Calculus Help!!!

Question

if f(2)=16, f' is continous, and (the integral of f2(at the bottom) and 6 as an exponent) f'(x)dx=19. what is the value of f(6)?

Answer 1

Step 1:

Write what's given So what's given is f(2)=16.

∫⁶₂ f'(x)dx=19

Step 2:

Find f(6) by solving definite integral.

∫⁶₂ f'(x)dx=f(6)-f(2)=16

f(6)-16=19

Step 3:

solve for f(6)

f(6)=19+16=35

so f(6)=35

Answer 2

Given f(2) = 16 and the integral of f'(x) from 2 to 6 is 19

-> we add these values because the integral represents the change in the function from x = 2 to x = 6.

So, f(6) = f(2) + (integral of f'(x) from 2 to 6)

= 16 + 19

= 35

Therefore, f(6) is 35.