ajedrezlaproa6j

2021-12-31

For what values of a is each integral improper?

${\int}_{a}^{4}\frac{x}{3x-1}dx$

Jonathan Burroughs

Beginner2022-01-01Added 37 answers

Consider the integral ${\int}_{a}^{4}\frac{x}{3x-1}dx$ .

Check whether the provided function is improper or not, find the point of infinite discontinuity.

Equate the denominator to zero.

3x-1=0

3x=1

$x=\frac{1}{3}$

The function has a discontinuity at$x=\frac{1}{3}$ , so the integral is improper on the interval [a,4] for $a\le \frac{1}{3}$ .

And the integral is improper when$a=-\mathrm{\infty}$

Thus, the given integral is improper for$a\le \frac{1}{3}$ or $a=-\mathrm{\infty}$ .

Check whether the provided function is improper or not, find the point of infinite discontinuity.

Equate the denominator to zero.

3x-1=0

3x=1

The function has a discontinuity at

And the integral is improper when

Thus, the given integral is improper for

Matthew Rodriguez

Beginner2022-01-02Added 32 answers

Now is

a=4

Vasquez

Expert2022-01-08Added 669 answers

Recall that an integral is improper if one of the limits is

We determined that the integral is improper for

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