Calculus Integration from -10 to 0 Yields a Strange Result

[MarcAReed]

Calculus Integration from -10 to 0 Yields a Strange Result [RESOLVED]

As part of a far greater enquiry, I found myself integrating:

$\int^{0}_{-10}x^3+2dx$

So, I began integrating the $x^3+2$ component, yielding the result of:

$[\frac{x^4}{4}+2x]^{0}_{-10}$

Which can then be set out as a subtraction, by:

$[\frac{0^4}{4}+2(0)]-[\frac{-10^4}{4}+2(-10)]$

The left term of the subtraction results in zero, whereas the right results in -2520, thus yielding the overall answer of:

$0--2520=0+2520=2520$

However, a most curious thing occurs, when I integrate the same definite integral on my calculator -- I get a different answer:

$-2480$

Not only can an area not be negative, but it defies my previous answer. So, now I have been lead to no other choice, but to ask you all for help, as to seeing where I went wrong.

Thankyou in advance, mes amis.

NOTE: I have a strong feeling that the mistake lies in either my own fault, or in my own lack of knowledge.

 

[skiller]

(-10)⁴ ≠-10⁴

 

[MarcAReed]

(-10)⁴ ≠-10⁴

Ah bon!

But my problem still stands, in that the result is that of a negative value -- should I just ignore the negative sign, and conclude that I must calculate the absolute value of integrals like this in future?

EDIT: To treat the integral maybe, as so:

$|(\int^{0}_{-10}x^3+2dx)|$

 

[Dickfore]

Ah bon!

But my problem still stands,

no, it does not.

 

[MarcAReed]

no, it does not.

You're very correct in your declarative statement -- I was a fool in not noticing that the value is negative because it is bellow y=0. I now, shall have to re-think my entire enquiry.

Thankyou, mes amis.

The issue is now resolved.