MarcAReed
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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.
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.
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