Approximate the integral and find the number of subintervals

Question

Approximating the integral - 5 to - 1 x²dx with the value of h=0.25 (step value or width), then the

number of subinterval is

a. 8

b. 4

c. 16

d. none of these

Answer 1

The length of the subinterval is the distance from -5 to -1 which is determined by | -5 - (-1)| = 4. If you think of the distance between to numbers on a horizontal line as "x-coordinate at the right minus x-coordinate at the left". -1 - (-5) equals 4 you do not have to think about the absolute value symbols.

Now the question is how many "0,25"s are contained in that distance? This is found by division. For example, how many 2's are contained in 8? 8/2 = 4.

So for this problem 4/ 0.25 = 4/ (1/4) = 4 (4) = 16.