Question

Calculus Help Please Explain.

Answer 1

@freckles

Answer 2

you are given f''
and you want to find f

Answer 3

if you integrate f'' just once you get f'

Answer 4

try that

Answer 5

and let me know what you get for f'

Answer 6

ok give me a minute.

Answer 7

So integrate the f''?

Answer 8

I would like to apply the condition for f' first
that condition being f'(0)=7

Answer 9

use this to find the constant value in your f'(x)

Answer 10

I integrated f'' and got x^3/3+C

Answer 11

ok and so f'(x)=x^3/3+C
and you are given f'(0)=7

Answer 12

f'(0)=0^3/3+C but f'(0)=7
so 0^3/3+C=7

Answer 13

find C
then we will integrate f' to find f and use f(0)=2 to find the constant of integration here

Answer 14

C=7

Answer 15

right so you have f'(x)=x^3/3+7
integrate f' to find f

Answer 16

x^4/12+Cx+C

Answer 17

Why is there two C's?

Answer 18

f(x)=x^4/12+7x+C

Answer 19

*x^4/12+Cx

Answer 20

ohhhh my bad i put C instead of 7 I frgot to plug in

Answer 21

now use f(0)=2 to find C
in f(x)=x^4/12+7x+C

Answer 22

by the way some people would feel OCD about calling this new constant of integration C when we called the old one C also

Answer 23

You could have wrote
x^4/12+Cx+D for f if you wanted
but not x^4/12+Cx+C

Answer 24

So anyways we have f(x)=x^4/12+7x+D
I guess I will use D instead
but anyways use f(0)=2 to find D

Answer 25

C=-2

Answer 26

how did you get C (or D whatver) is -2?

Answer 27

C=-5***

Answer 28

0^4/12+7(0)+C=2 ?

Answer 29

typo

Answer 30

0+0+C=2
so C=?

Answer 31

Oh I forgot to plug in 0 for x by the 7 it should be C=2

Answer 32

so then y=f(x) is ?

Answer 33

this one I have no clue where to start.

Answer 34

\[f''(x)=x^2 \\ f'(x)=\frac{x^3}{3}+C \\ \text{ use } f'(0)=7 \text{ \to find } C \\ f'(0)=\frac{0^3}{3}+C=7 \implies C=7 \\ f'(x)=\frac{x^3}{3}+7 \\ f(x)=\frac{x^4}{3(4)}+7x+D \\ f(x)=\frac{x^4}{12}+7x+D \\ \text{ use } f(0)=2 \text{ \to find } D \\ f(0)=\frac{0^4}{12}+7(0)+D=2 \implies D=2 \\ \text{ so } f(x)=\frac{x^4}{12}+7x+2\]

Answer 35

just use addition/difference law for integration
and use constant multiple rule for integration

Answer 36

Gotcha

Answer 37

\[\int\limits (a f(t)+b g(t))dt \\ =\int\limits a f(t) dt + \int\limits b g(t) dt \\ =a \int\limits f(t) dt + b \int\limits g(t) dt \]

Answer 38

then plug in

Answer 39

and perform order of operations

Answer 40

for the next one?

Answer 41

what next one

Answer 42

I the last one I seen was 27

Answer 43

that's the same problem

Answer 44

did you mean to post another one

Answer 45

Oh ok... So just plug in?

Answer 46

just use addition/difference law for integration
and use constant multiple rule for integration
then plug in
then order of operations

Answer 47

I gave an example above on how to use addition/difference and constant multiple rule for integration

Answer 48

Ok I'll try it .

Answer 49

I have to go
should be pretty easy though
it is like them asking you to evaluate -24X-2Y
when X=15/4 and Y=3/2

Answer 50

I don't get it..

Answer 51

\[\int\limits_1^2 (-24t^3-2t) dt \\ \int\limits_1^2 (-24t^3)dt -\int\limits _1^2 (2t )dt \]
did you try to apply the difference/addition rule for integration?

Answer 52

now bring out those constants for each
and just plug in the values given

Answer 53

ohhhhh ok I think i see it now... I'll catch ya later :)Thanks again for the help.