The area bounded by 𝑥=𝑦2−2 and 𝑥=𝑒𝑦  between  𝑦=−1 and 𝑦=1 is revolved about the line 𝑦=1. The Volume integral for the solid generated is

Question

The area bounded by 𝑥=𝑦2−2 and 𝑥=𝑒𝑦  between  𝑦=−1 and 𝑦=1 is revolved about the line 𝑦=1. The Volume integral for the solid generated is
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Solution 1

The volume of a solid of revolution can be found using the formula for the volume of a solid of revolution about the y-axis:

V = ∫[a,b] π (outer function)^2 - π (inner function)^2 dy

Here, the outer function is ey and the inner function is y^2 - 2. The limits of integration are y = -1 to y = 1.

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