Integration - AP Calc AB

Question

Use the limit definition to evaluate the definite integral fnInt (2x^3+3)dx lower bound-2 upper bound - 6. (Use right endpoints for c sub-i and equal subintervals

Answer 1

Hi Bull,

 

The width of each of n equal sub-intervals is given by (6-2)/n = 4/n.

 

The right-hand endpoint of each sub-interval is given by 2+4i/n where i it the ith sub-interval.

 

To find the height of the rectangle at the right-hand endpoint plug that expression into the function definition, which gives: 2(2+4i/n)³ + 3.

 

So the area of each rectangle is given by A_i = 4/n times the expression in the previous sentence. Pretty messy.

 

https://www.youtube.com/watch?v=aSShem5RnzE&t=46s

 

What we want is the lim as n-> inf of Sum A_i. I am taking a chance that WyzAnt will not delete this answer because of the link I have included above. It is a link to a video that I created to help a student with evaluating area under f(x) = x³ from 0 to 3.