Evaluate the following integrals or stat that they diverge.

${\int}_{0}^{\mathrm{\infty}}{e}^{-ax}dx,a>0$

tricotasu
2021-08-14
Answered

Evaluate the following integrals or stat that they diverge.

${\int}_{0}^{\mathrm{\infty}}{e}^{-ax}dx,a>0$

You can still ask an expert for help

yunitsiL

Answered 2021-08-15
Author has **108** answers

Step 1

Any integral is an improper integral if it follows these two conditions:

1) One of the limit of the integral reaches to infinity.

2) The function whose integral has to be calculated has to be unbounded. This means that it should not be ending at a point. It has to be everlasting.

The integral of these types have no special rule to calculate. These are just like normal integral.

Integration is done below:

Step 2

Any integral is an improper integral if it follows these two conditions:

1) One of the limit of the integral reaches to infinity.

2) The function whose integral has to be calculated has to be unbounded. This means that it should not be ending at a point. It has to be everlasting.

The integral of these types have no special rule to calculate. These are just like normal integral.

Integration is done below:

Step 2

asked 2021-11-19

Use integration by parts to find the integral:

$\int 7x\mathrm{ln}xdx$

asked 2022-03-18

Can anyone help to integrat this function please?

$ic{\int}_{-1}^{1}\left(\frac{-2}{x}\frac{1}{1+{\left(\frac{tc}{x}\right)}^{2}}\right)dt$

C>0, x>0 and i the imaginary part

Not really sure how to go about integrating it.

C>0, x>0 and i the imaginary part

Not really sure how to go about integrating it.

asked 2021-06-03

Find formulas for the functions represented by the integrals.

${\int}_{-\frac{\pi}{4}}^{x}{\mathrm{sec}}^{2}0d0$

asked 2020-10-26

Convert the above indefinite integrals into definate integrals using the intervals $[0,1]$ .

(a)$\int \sqrt{{a}^{2}-{x}^{2}}dx$

(b)$\int \sqrt{1-{x}^{2}}dx$

(a)

(b)

asked 2021-11-19

Evaluate the definite integral.

${\int}_{0}^{1}\frac{7}{1+{x}^{2}}dx$

asked 2021-05-18

Find all zeros of the polynomial

asked 2021-08-09

Evaluate the definite integral.

${\int}_{0}^{\sqrt{2}}x{e}^{\frac{-{x}^{2}}{2}}dx$