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By integrating along the y-axis, calculate the area bound between the y-axis and the function y = x³ for -1 <= y <= 1

User Bdls
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Final answer:

To calculate the area bound between the y-axis and the function y = x³ for -1 ≤ y ≤ 1 by integrating along the y-axis, we will integrate with respect to y and use the power rule of integration.

Step-by-step explanation:

To calculate the area bound between the y-axis and the function y = x³ for -1 ≤ y ≤ 1 by integrating along the y-axis, we will integrate with respect to y. Since y = x³, we can rewrite the equation as x = y^(1/3). The limits of integration are -1 and 1. So, the area is given by the integral of x with respect to y from -1 to 1:

A = ∫ x dy = ∫ (y^(1/3)) dy

Using the power rule of integration, we can find the antiderivative of y^(1/3), which is (3/4)y^(4/3). We can then evaluate the integral:

A = [ (3/4)y^(4/3) ] from -1 to 1

Substituting the limits of integration:

A = (3/4)(1^(4/3) - (-1)^(4/3)) = (3/4)(1 + 1) = (3/4)(2) = 3/2

User Flashrunner
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