What am I dong wrong here?

[Alexandra Fabiello]

Homework Statement

If y' = 6x(x²+2)² and y = 25 when x = 1, what is the value of y when x = -1?

Homework Equations

N/A

3. The Attempt at a Solution [/B]

∫6x(x²+2)²dx = 2x(x²+2)³

(1² + 3)³ + 2(1) + c = 25

1 + 2 = 3 and 2(1) = 2 and 3³ = 27, so 27*2 + c = 25 so 54 + c = 25, therefore c = 25-54 = -29

Now substitute x = -1

(-1) squared is 1 and 2(-1) = -2, so 27*-2 = -54, so -54 - 29 = y = -83

WileyPlus tells me it's wrong.

What is wrong with this?

 

[SammyS]

Homework Statement

If y' = 6x(x²+2)² and y = 25 when x = 1, what is the value of y when x = -1?

Homework Equations

N/A

3. The Attempt at a Solution [/B]

∫6x(x²+2)²dx = 2x(x²+2)³

You need a constant of integration in that result.

Also, you made a mistake in your integration.

What is the derivative of y = 2x(x²+2)³ + C ?

(1² + 3)³ + 2(1) + c = 25

1 + 2 = 3 and 2(1) = 2 and 3³ = 27, so 27*2 + c = 25 so 54 + c = 25, therefore c = 25-54 = -29

Now substitute x = -1

(-1) squared is 1 and 2(-1) = -2, so 27*-2 = -54, so -54 - 29 = y = -83

WileyPlus tells me it's wrong.

What is wrong with this?

 

[Alexandra Fabiello]

You need a constant of integration in that result.

Also, you made a mistake in your integration.

What is the derivative of y = 2x(x²+2)³ + C ?

OH! *smacks self* Never mind...

And I just forgot to type in the + c; you'll see in my calculations that it appears there, sorry.

EDIT: Thanks, BTW, like a LOT!

 

[Alexandra Fabiello]

Thanks a lot, SammyS!