- #1

ZeroPivot

- 55

- 0

how about integrals? can u take the inverse for instance: integral(f(x)dx)

turn it into integral((1/f(x))dx)^-1) get the answer and then reverse it back?

when can u or cant you take the inverse???

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- Thread starter ZeroPivot
- Start date

- #1

ZeroPivot

- 55

- 0

how about integrals? can u take the inverse for instance: integral(f(x)dx)

turn it into integral((1/f(x))dx)^-1) get the answer and then reverse it back?

when can u or cant you take the inverse???

- #2

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 970

Do you have some specific reason for asking about the inverse of an integral? In general the inverse of the integral of a function is NOT the integral of the inverse of the function. Your last expression has an unmatched right parenthesis so it is hard to tell exactly what you intend.

- #3

ZeroPivot

- 55

- 0

something easy say y=2x+1 and u want the integral integral(2x+1)dx can u switch it around and say (integral(1/(2x+1))dx)^-1, are there any integrals u can do this to or is it a no no?

- #4

verty

Homework Helper

- 2,185

- 198

something easy say y=2x+1 and u want the integral integral(2x+1)dx can u switch it around and say (integral(1/(2x+1))dx)^-1, are there any integrals u can do this to or is it a no no?

Integrate that and see what you get. It'll have nothing to do with the inverse of y = 2x+1.

- #5

Mandelbroth

- 611

- 24

You can take the inverse of any function. (pause for shock value :tongue:)

how about integrals? can u take the inverse for instance: integral(f(x)dx)

turn it into integral((1/f(x))dx)^-1) get the answer and then reverse it back?

when can u or cant you take the inverse???

HOWEVER, it is important to note that the inverse of a function is not necessarily a function. For example, consider the ##\sin## function. Since ##\sin(x)=\sin(x+2\pi)##, ##\sin^{-1}(\sin(x))## will not be unique. In fact, ##\sin^{-1}(\sin(x))=x+2\pi n##, where ##n\in\mathbb{Z}##.

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