Question

What is the correct representation of this question, pls? (diagram incl)

Answer 1

@ganeshie8 pls take a look

Answer 2

Initial Value Problem

Answer 3

OK

Answer 4

Initial Value is :
when x =3, I = 25

Answer 5

Got confused with the "I" there

Answer 6

Hmmm, first course in Calculus II

Answer 7

\(\large I = \int 4x^2 dx = \frac{4x^3}{3} + c\)

Answer 8

we're done wid calc :)

plugin x = 3, and I = 25
and solve \(c\)

Answer 9

Thank you very much @ganeshie8

Answer 10

np :)

Answer 11

Our course material excluded this, but the lecturer thought it wise to bring it up in test assignments.

Answer 12

oh... IVP is an important problem... should atleast do 1-2 problems...
important for differential-equations later...

Answer 13

So, basically, we take the integral of 4x^2 and then subst. values of I and x in the equation, right?

Answer 14

yes,
taking the indefinite-integral gives u constant \(c\)

Answer 15

we need to find the numerical value of that constant using the "Initial Value" given

Answer 16

thats all.

Answer 17

so, basically two steps :
1) take the indefinite-integral
2) find out numerical value of constant and plugin

Answer 18

Thanks, buddy :3

Answer 19

u wlc :)

Answer 20

How about this \[\int\limits_{}^{} 2e^x dx\]

Answer 21

I know the integral is simply \[2e^x\], but then how do I subst. x?

Answer 22

indefinite integral is : \(2e^x + c\)

Answer 23

dont forget the integration constant :)

Answer 24

yes ... + C

Answer 25

Are you given any "Initial Value" ?

Answer 26

50.2

Answer 27

and x = 3

Answer 28

when x = what ?

Answer 29

okay good :)
so substitute x = 3 and equate it to 50.2

Answer 30

\(\large 2e^{3} + c = 50.2\)

solve \(c\)

Answer 31

e^3 there, is my bane

Answer 32

Never mind @ganeshie8 a calculator can do that. Thank you once more.

Answer 33

or leave it as :
\(c = 50.2 - 2e^3\)

Answer 34

so the integral becomes :

\(2e^x + 50.2 - 2e^3\)

Answer 35

You're very good with calculations, I must confess. Are you still in college or PG?

Answer 36

Or, if u want it look more neat u may do below :

Answer 37

\(\large I = \int 2e^x = 2e^x + c = c_1e^x\)

\(\large c_1e^3 = 50.2 \implies c_1 = \frac{50.2}{e^3}\)

plugin this value in \(I\)

\(\large I = \frac{50.2}{e^3}e^x = 50.2e^{x-3}\)

Answer 38

thats another solution.

btw, both are correct ! but i prefer the second one ... as it looks in standard exponential equation form : \(Ae^{t}\)

Answer 39

nvm, it wont work... please disregard second solution :|

Answer 40

Yeah, looks standard. I'll find time to read up on that.

Answer 41

I wanted to put it in standard form, but leave it for now... lol the second solution doesnt look right

Answer 42

Okay. The other question is maybe personal if am right. So I can understand...