Question

I am going to practice some improper integrals. If you see some errors please correct me.

Answer 1

\[\int\limits_{2}^{\infty }\frac{1}{x^3}dx\]just posting the problem. Now I will do it.

Answer 2

\[\lim_{a \rightarrow \infty}~\int\limits_{2}^{a}\frac{1}{x^3}dx\]\[\lim_{a \rightarrow \infty}~\int\limits_{2}^{a}~\frac{-2}{x^2}{\LARGE|}^{a}_{2}\]\[\lim_{a \rightarrow \infty}~\frac{-2}{a^2}-\lim_{a \rightarrow \infty}~\frac{-2}{2^2}\]\[0+\lim_{a \rightarrow \infty}~\frac{1}{2}\]
answer is 1/2.

Answer 3

write it as x^-3

Answer 4

lol, I know that if I am solving improper integrals. Or else I wouldn't be solving these.

Answer 5

He just means to give you a hint, as your anti-derivative is wrong. Rewriting it might help you see the error

Answer 6

no it is correct.

Answer 7

the power rule is\[\int\limits_{ }^{ }x^{n}=\frac{x^{n+1}}{n+1}+C\]and in this case n+1 is -3+1 which is -2.

Answer 8

no your antiderivative is wrong

Answer 9

yes, I see it

Answer 10

I wrote that -2 on top

Answer 11

sorry

Answer 12

i think its