Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = x3 - 3x2 + 2x and the x-axis?

a. one half times the integral from 0 to 2 of the quantity x cubed minus 3 times x squared plus 2 times x, dx

b. 2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx

c. the integral from 0 to 1 of the quantity squared of x cubed minus 3 times x squared plus 2 times x, dx

d. the integral from 0 to 2 of the quantity x cubed minus 3 times x squared plus 2 times x, dx

Question

Xavier Duffy

Mathematics

28 July, 06:39

Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = x3 - 3x2 + 2x and the x-axis?

a. one half times the integral from 0 to 2 of the quantity x cubed minus 3 times x squared plus 2 times x, dx

b. 2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx

c. the integral from 0 to 1 of the quantity squared of x cubed minus 3 times x squared plus 2 times x, dx

d. the integral from 0 to 2 of the quantity x cubed minus 3 times x squared plus 2 times x, dx

+3

Answers (1)

Know the Answer?

Mariela Leon · Answer 1

By definition, the integral of a function represents the area under the curve. We have then for the function

y = x ^ 3 - 3x ^ 2 + 2x

The area under the curve and the x axis is:

Int ((x ^ 3 - 3x ^ 2 + 2x) * dx). between 0 and 2

answer

d. The integral from 0 to 2 of the quantity x cubed minus 3 times x squared plus 2 times x, dx