Question

http://prntscr.com/9rsz4e

Answer 1

You are given that f(0)=3, and you need to find f(5).

Answer 2

\(\color{#000000}{f(x)=\displaystyle \int f'(x)~dx }\)

agree?

Answer 3

yes

Answer 4

STEP 1:
You can integrate the 1st part of the f'(x), to find
the f(x) on the interval [0,2). Then find constant
C based on the initial value, f(0)=3.

STEP 2:
Next, integrate the 2nd part of f'(x). This will give
you the f(x) on the interval [2,5]. Then, instead of
constant C, you will put the value that you found
for constant C from step 1.

STEP 3:
After you have found the f(x) on the interval [2,5],
plug in 5 into this function to find f(5).

Answer 5

Can i show u what i did and see if it's correct?

Answer 6

Yes, sure, go ahead:)

Answer 7

\[\int\limits_{0}^{5}f'(x)dx=f(5)-f(0)\]
\[\int\limits_{0}^{5}f'(x)dx=f(5)-3\]
\[\int\limits_{0}^{5}f'(x)dx+3=f(5)\]
\[3+[(-2*4)+(-1/2*2*4)+(1/2*1*2)]=f(5)\]
3-8-4+1=f(5)
-8=f(5)

Answer 8

Good, very clever!
You applied the standard theorem of calculus, and then the rule that the integral of any function from x=a to x=b, is the area between the x-axis and the curve/function on the interval [a,b].

Answer 9

Yay! Just wanted to make sure what i was doing was correct