Integration of a polynomial problem

[MartinJH]

Hi,
I'm using KA Stroud 6th edition (for anyone with the same book, P407) and there is a example question where I just can't seem to get the answer they have suggested:

Homework Statement

[/B]
Question:
Determine the value of I = ∫(4x³-6x²-16x+4) dx
when x = -2, given that at x = 3, I = -13
Their answer is when x = -2, I = 12.

The Attempt at a Solution

[/B]
I found the integral: I = ∫(4x³-6x²-16x+4) dx = x⁴-2x³-8x²+4x + C
and then substituted x for 3 and getting:
-13 = -33 + C
thus:
C = 20
Now when I replace x with -2, plus the constant, I get:
-2⁴-2(-2)³-8(-2)²+4(-2) + 20 = -20

I'm a few days into Integrals so I feel I may be doing something daft?

Many thanks.

 

[Mark44]

Hi,
I'm using KA Stroud 6th edition (for anyone with the same book, P407) and there is a example question where I just can't seem to get the answer they have suggested:

Homework Statement

[/B]
Question:
Determine the value of I = ∫(4x³-6x²-16x+4) dx
when x = -2, given that at x = 3, I = -13
Their answer is when x = -2, I = 12.

The Attempt at a Solution

[/B]
I found the integral: I = ∫(4x³-6x²-16x+4) dx = x⁴-2x³-8x²+4x + C
and then substituted x for 3 and getting:
-13 = -33 + C
thus:
C = 20
Now when I replace x with -2, plus the constant, I get:
-2⁴-2(-2)³-8(-2)²+4(-2) + 20 = -20

I'm a few days into Integrals so I feel I may be doing something daft?

Many thanks.

Your work is fine except for one minor thing. At the end you wrote -2⁴ instead of (-2)⁴. In the first, 2 is raised to the 4th power, and then you take the negative, resulting in -16. In the latter, -2 is raised to the 4th power, resulting in +16.

 

[MartinJH]

That was an honest slip. I appreciate there is a difference between them both.
I finally got the answer, it was a case of not respecting the brackets and powers... I need a break.

Thanks for pointing that out and explaining! :)

 

[LCKurtz]

HEY! I thought micromass's avatar was retired.

 

[MartinJH]

HEY! I thought micromass's avatar was retired.

I assume that is for me? :). I use this logo for most online things. EEVBlog, my Steam account etc etc. I was thinking about using Floyds new album cover.

 

[LCKurtz]

Yes, but it was really directed at the old timers, sort of tongue-in-cheek. Turns out one of our previous highly regarded members used to use that logo. Nothing to worry about though.

 

[MartinJH]

Yeah, that's cool. I Understand :).