Question

did you know about improper integrals?

Answer 1

Yes....

Answer 2

thank you... can you give some example?

Answer 3

There are two types of improper integrals...

Ones where your limits go to infinity

And

Ones where where the integrand isn't continuous on the interval over which you're integrating.

Answer 4

how to graph the improper integral?

Answer 5

Infinite limits: \[
\int_a^\infty f(x)dx = \lim_{t\to \infty}\int_a^t f(x)dx\\

\int_{-\infty}^a f(x)dx = \lim_{t\to -\infty}\int_t^a f(x)dx\\

\int_{-\infty}^\infty f(x)dx = \lim_{t\to -\infty}\int_t^a f(x)dx+ \lim_{t\to \infty}\int_a^t f(x)dx\\
\]

Answer 6

can you give some example the improper integral?

Answer 7

Discontinuous type: Suppose \(f(x)\) is not continuous at \(c\) and \(c\in[a,b]\) \[
\int _c^bf(x)dx = \lim_{t\to c^-}\int_t^bf(x)dx\\

\int _a^cf(x)dx = \lim_{t\to c^+}\int_t^cf(x)dx\\

\int _a^bf(x)dx = \lim_{t\to c^-}\int_t^bf(x)dx+ \lim_{t\to c^+}\int_t^cf(x)dx\\
\]

Answer 8

You want an example??

Answer 9

..yes..

Answer 10

Okay well the Laplace transform is an example... \[
\mathcal{L}\{f(t)\} = \int_0^\infty e^{-st}f(t)dt
\]It uses an improper integral of the infinite type.

Answer 11

how to solve your given example?

Answer 12

It depends on the function.

Answer 13

If you know how to do integrals and you know how to do limits, then you can do improper integrals... otherwise you are in over your head.