Question

Evaluate: LaTeX: \int^8_6\frac{4}{\left(x-6\right)^3}dx ∫ 6 8 4 ( x − 6 ) 3 d x a. Diverges LaTeX: \left(\infty\right) ( ∞ ) b. Diverges LaTeX: \left(-\infty\right) ( − ∞ ) c. 0 d. LaTeX: \frac{1}{4} 1 4 e. LaTeX: \frac{2}{9} 2 9

Answer 1

I could not properly read this but here was what I could make out

Explanation:

Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)

home this helped ;)

Answer 2

It diverges to positive infinity

Explanation:

I see it was 4/(x-6)^3 not 4(x-6)^3... but still can't make out everything else.

`\int_6^8 (4)/((x-6)^3) dx`

The integrand does not exist at x=6.

`\int_6^8 (4)/((x-6)^3) dx`

`\lim_(z \rightarrow 6^(+) ) \int_z^8 4(x-6)^(-3) dx`

`\lim_(z \rightarrow 6^(+) )(4(x-6)^(-2))/(-2) |_z^8dx`

`\lim_(z \rightarrow 6^(+) )[(4(8-6)^(-2))/(-2) -(4(z-6)^(-2))/(-2) ]`

`(1)/(-2) - -\infty`

`\infty`

So it diverges