# How do you use limits to find the area between the curve #y=2x^3# and the x axis from [1,5]?

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To find the area between the curve (y = 2x^3) and the x-axis from (x = 1) to (x = 5), you can use definite integration. First, find the points of intersection between the curve and the x-axis by setting (y = 0) and solving for (x). Then, integrate the absolute value of the function from the smaller x-value to the larger x-value within the given interval. The integral expression for this area would be:

[ \text{{Area}} = \int_{1}^{5} |2x^3| , dx ]

Solve this integral to find the area.

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