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anonymous
 one year ago
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = x(6 − x)2
for my answer I got X^4/44x^3+18x^2+C is this right?
anonymous
 one year ago
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = x(6 − x)2 for my answer I got X^4/44x^3+18x^2+C is this right?

This Question is Closed

freckles
 one year ago
Best ResponseYou've already chosen the best response.2Did you find the derivative to check yourself?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2To keep things simple, you may try usubstitution \(u = 6x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no i didn't find the derivative to check my answer, i would find the derivative of my problem right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2yeah you can differentiate your answer and see if it is x^312x^2+36x which is the form I think you put it in to integrate (by the way if you have heard of substitutions to make integrals like this nicer looking (or I mean easier) at ganeshie8's note )

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2nvm if you haven't heard of usubstition before your work looks good, i presume you have used the formula for antiderivative of \(x^n\) to double check, differentiate the answer as freckles said

freckles
 one year ago
Best ResponseYou've already chosen the best response.2he might heard of it I don't know

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im not sure i have, but i took the derivative and got x^212x+36x :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah its just that i had x(x^212x+36)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2and yes I already checked your answer integrating thingy but your problem said to also check your solution by differentiating so now you done both things your problem asked for

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0got it right! thanks!!

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2how do you know ` x(x^212x+36) ` is same as the original function ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2that might be a dumb q hmm

freckles
 one year ago
Best ResponseYou've already chosen the best response.2x(6x)^2 think he expanded the square thingy first

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Ahh looks great she :D

freckles
 one year ago
Best ResponseYou've already chosen the best response.2do you want to see the sub thingy mentioned by ganeshie8 for fun?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Its okay! sure is it easier than finding the derivative?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\int\limits x (6x)^2 dx \\ \text{ Let } u=6x \\ \frac{du}{dx}=01 \\ \frac{du}{dx}=1 \\ du=1 dx \\ \text{ multiply both sides by 1 } \\ du=dx \\ \text{ now recall if } u=6x \text{ then } x=6u \\ \text{ so we have } \\ \int\limits x (6x)^2 dx=\int\limits (6u)u^2 (du) \\ =\int\limits (u6)u^2 du\] so now you have less multiplication to do

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[=\int\limits (u6)u^2 du =\int\limits (u^36u) du=\frac{u^4}{4}3u^2+C \\ \text{ now remember } u=6x \\ \text{ so you have } \\ =\frac{(6x)^4}{4}3(6x)^2+C\] and it is less multiplication if you get to leave your answer like this :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[ x(6 − x)^2 = x(x^212x+36) = x^312x^2+36x \]Then use power rule. No tricks needed. Your antiderivative looks correct.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay, I didnt understand the substitution part at first, but i get it now! thanks for explaining!

freckles
 one year ago
Best ResponseYou've already chosen the best response.2oops I didn't multiply correclty

freckles
 one year ago
Best ResponseYou've already chosen the best response.2my answer is off because when I did 6(u^2) I put 6u and so I integrated the wrong thingy

freckles
 one year ago
Best ResponseYou've already chosen the best response.2but that is sorta how works above if you can multiply correctly :p

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2you should ask why on earth substitution is any better than your original method @gaba

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2try this if you're loving antiderivatives : \[\int x(6x)^{9999999}\,dx = ?\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm deff not loving them lol so Im working on this right now, Find the most general antiderivative of the function 2rootx+6cosx I got 4x^1/2+6sinx

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im not sure i did it right though

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2differentiate your answer and see if you get back the original function

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2also what happened to the constant, C

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0nvm I just did it again and got 4x^3/2/3 +6 sinx +C

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2you're doing calculus, that means you're not in highschool anymore time to use proper notation

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.24x^ `3/2/3` +6 sinx +C what does that even mean

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0[(4x^3/2)/3] +6sinx+C Btw you can take calculus in high school, just saying

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Much better, but still it is not mathematically correct

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2pretty sure you meant [(4x^3/2)/3] +6(sinx)+C

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2differentiate that and see if you get back the original function (there is a mistake, so you wont get back the original function)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why is it +6(sin(x)) and not sin(x)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[f(x)=2 \sqrt{x}+6 \cos(x) \\ \text{ or we can write } \\ f(x)=2 x^\frac{1}{2}+6 \cos(x)\] is this what you are playing with?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2anyways ( ? )'=cos(x) the ?=sin(x) right? (sin(x))'=cos(x) so the antiderivative of cos(x) is sin(x)+C if I had ( ? )'=sin(x) the ?=cos(x) (cos(x))'=sin(x) so the antiderivative of sin(x) is cos(x)+C now if you had ( ? )'=cos(x) then ?=sin(x) (sin(x))'=cos(x) so the antiderivative of cos(x) is sin(x)+C anyways you had find the antiderivative of 2x^(1/2) which looks like you were going for: 4x^(3/2)/3 +k but to find the antiderivative of 6cos(x) you need to recall what can you take derivative of that will give you 6cos(x) you can bring down the 6( and put the antiderivative of cos(x)) here )

freckles
 one year ago
Best ResponseYou've already chosen the best response.2forgot to put + some constant at the end there

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay, is that to make sure I had it right I checked on mathway for the derivative of cos(x) and it said it was sin(x) (which is what I thought it was before checking so it made sense) but i typed in +sin(x) and got it right, so thanks for explaining everything!

freckles
 one year ago
Best ResponseYou've already chosen the best response.2oh so you got derivative and antiderivative mixed up

freckles
 one year ago
Best ResponseYou've already chosen the best response.2but just so you know if it was taking derivative of 6cos(x) you would put 6sin(x) and not 6sin(x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2but yeah antiderivative of 6cos(x) would be 6sin(x) since the derivative of 6sin(x) is 6cos(x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2the antiderivative of 6cos(x) would be 6sin(x)+C since the derivative of 6sin(x)+C is 6cos(x) *

freckles
 one year ago
Best ResponseYou've already chosen the best response.2the most general antiderivative *

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay I understand now! thanks a lot!!
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