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

Answer:

It diverges to positive infinity  

Step-by-step explanation:

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

$\int_6^8 \frac{4}{(x-6)^3} dx$

The integrand does not exist at x=6.

$\int_6^8 \frac{4}{(x-6)^3} dx$

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

$\lim_{z \rightarrow 6^{+} }\frac{4(x-6)^{-2}}{-2} |_z^8dx$

$\lim_{z \rightarrow 6^{+} }[\frac{4(8-6)^{-2}}{-2} -\frac{4(z-6)^{-2}}{-2} ]$

$\frac{1}{-2} - -\infty$

$\infty$

So it diverges