What is wrong with the following calculation?
int_{-2}^{1}\frac{ 1 }{ x^4 }dx=\frac{ -1 }{ 3x^3 }]^1(-2)below=\frac{ -1 }{ 3 }-\frac{ 1 }{ 24 }=\frac{ -9 }{ 24 }

Question

What is wrong with the following calculation?
int_{-2}^{1}\frac{ 1 }{ x^4 }dx=\frac{ -1 }{ 3x^3 }]^1(-2)below=\frac{ -1 }{ 3 }-\frac{ 1 }{ 24 }=\frac{ -9 }{ 24 }

anonymous · Answer

This is the question.
$$\int\limits_{-2}^{1}\frac{ 1 }{ x^4 }dx$$

zarkon · Answer

what happens when x=0

anonymous · Answer

it would be undefined?

zarkon · Answer

so this integral is an improper integral

anonymous · Answer

what? I don't quite understand...

zarkon · Answer

was all that work above given and you are to tell why it is wrong?

zarkon · Answer

or is it your work?

anonymous · Answer

It's not my work, it's from the textbook

zarkon · Answer

to use the FTC the integrand (the thing inside the integral) must be continuous on the interval you are integrating over

anonymous · Answer

okay...

zepdrix · Answer

still confused? :o

anonymous · Answer

yes... :(

zepdrix · Answer

1/x^4 has an asymptote at x=0, ya? :o

anonymous · Answer

yes

zepdrix · Answer

so our function is not continuous over the given interval.|dw:1433734647150:dw|See the problem the 0 is creating for us? +_+