Find F'(x) when F(x)= the integral of (1/t^6)dt on the interval [2,x^2].

We have the problem ∫1/t^6 dt on the interval [2,x].
The problem is really ∫t^(-6) dt on the interval [2,x].

The answer is found by adding one to the exponent and dividing by the new exponent.
That gives t^(-5)/(-5) evaluated from 2 to x.
That becomes [x^(-5) - 2^(-5)]/(-5).

When taking a square to another power, multiply the exponents.
When taking 2^5, 32 is gotten.  When taking to the -5, 1/32 is then gotten.

Switch the two terms in the numerator to eliminate the negative sign in the denominator.
That gives [1/32 - 1/x^10]/5.

This can be rewritten by combining the two fractions.
This gives (x^10 - 32)/(160x^10).  


All Answers

Answers by Expert:

Ask Experts




Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology (reproduction, insusion of chemicals into bloodstream).


Experience in the area: I have tutored students in all areas of mathematics since 1980. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Maybe not a publication, but I have respond to well oveer 8,500 questions on the PC. Well over 2,000 of them have been in calculus.

I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few courses at college a year early.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2016 All rights reserved.