Question

Integration

Answer 1

For a continuous function f(x), f(1)=11, and \[\int\limits_{1}^{5}f'(x)dx = 9\] determine f(5).

Answer 2

@freckles

Answer 3

do you know what
\[\int\limits f'(x) dx=?\]

Answer 4

9

Answer 5

oh wait that is the indefinte integral

Answer 6

that isn't what i'm asking
your question has definite integral in it while I asked about indefinite integral

Answer 7

ok you got it :p

Answer 8

I mean you figured out I was asking about a indefinite integral

Answer 9

F(x)

Answer 10

you do know the derivative of f(x) is f'(x)

Answer 11

so the integral of f'(x) is f(x)+C

Answer 12

\[\int\limits f'(x) dx=f(x)+C\]

Answer 13

in definite integrals we don't need the C since they get cancel out in the simplifcation of a definite integral

Answer 14

\[\int\limits_a^b f'(x) dx=f(x)|_a^b =f(b)-f(a)\]

Answer 15

can you show me your equation you have after evaluating your definite integral on your left hand side of your equation you wrote

Answer 16

The left-hand side like Reiman sums?

Answer 17

no no

Answer 18

you have an equation

Answer 19

for example a=b
the right hand expression of the equation is b
and left hand expression of the equation is a

Answer 20

Oh duh

Answer 21

your left hand side looks like this
\[\int\limits_1^5 f'(x)\]

Answer 22

I'm asking you to evaluate the definite integral here

Answer 23

we dont have f'(x) though

Answer 24

here is a hint:
\[\int\limits_1^5 f'(x) dx=f(x)|_1^5=....\]

Answer 25

9 right?

Answer 26

don't look at the right hand side yet

Answer 27

I'm trying to get you the write the left hand side as f(5)-f(1)

Answer 28

4

Answer 29

f(5)-f(1)=9
you are given f(1)=11
f(5)-11=9
solve for f(5)

Answer 30

oh yah now i remember this

Answer 31

you are going to add what to both sides to do this?

Answer 32

20

Answer 33

yes f(5)=11+9
f(5)=20

Answer 34

do you have any questions on this one
(I'm going to leave you if you don't)

Answer 35

My computer hit a lag spike

Answer 36

okay im good thanks

Answer 37

enjoy your lunch

Answer 38

I think I seen @zepdrix on
he is really good at math too

Answer 39

Peace

Answer 40

Yup im a fan