Mathematics

Problem

The region

R

is bounded by the curves

y = x^2

and

y = 2x

. a. (i) Write a definite integral with respect to

x

that gives the area of

R

. b. (ii) Write the corresponding definite integral(s) with respect to

y

that give the same area. c. (iii) Evaluate both and verify that the two results are equal.