Lucas S.

asked • 11/10/23

Evaluate the integral by interpreting it in terms of areas

∫(x-√(25-x2)dx, on the integral, [5,-5]

1 Expert Answer

By:

Ellsworth J. answered • 11/10/23

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Lucas S.

Thank you so much! Can I ask how the base is 10? I thought that since y=x is what is above the x-axis, that the base would be the same as the height?
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11/10/23

Ellsworth J.

In fact, I'm going to amend my answer. The contribution of the first function is ZERO, which you can get from the formula, or just doing it intuitively. The "negative area" below the x-axis in [-5, 0] cancels out the positive area above the x-axis on [0, 5]. So only the semicircle contributes to the final answer. That's what I get for trying to do calculus at 4 in the morning! :)
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11/10/23

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