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

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

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Answer 1 · 2018-04-29T18:44:33

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

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

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

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

$\int_{0}^{2} y^{3} d y$ $int_0^2y^3dy$

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

1 Answer

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