Question

Write a definite integral that yields the area of the region. (Do not evaluate the integral.)?

Answer 1

This is different from the normal area integral, which calculates the `y` distance from the `x`-axis as a function of `x`.

Instead, we are measuring a an infinite number of horizontal lines, which are the `x` distances from the `y`-axis, determined as a function of `y`.

Since we measure as a function of `y`, the integral will range over the values of `y`. Here the `y` values start at `0` and end at `2`.

The function that gives the `x` distance is `x=y^3`. So we want the integral

`int_0^2y^3dy`