midpoint rule to aproximate the integral

Question

Use the Midpoint Rule with  to approximate the integral 

∫√(x³+7) dx ≈

from 2 to 10



Answer 1

Figure out the midpoints of the intervals that are created by dividing the domain of x by the number of intervals. Intervals will be (10 - 2)/4 = 2 large . The interval edges are 2, 4, 6, 8, 10 and the midpoints are 3, 5, 7, 9.

In order to approximate the integral add the areas of the four rectangles formed that are f(midpoint) high and x interval across.

Here is the area of the first rectangle is f(3)* 2 = sqrt(3³ + 7) * 2

I'll leave the rest to you.