# If the infinite curve y = e^{-4x}, \quad x \gt 0 , is rotated about the x-axis, find the area...

## Question:

If the infinite curve {eq}y = e^{-4x}, \quad x \gt 0 {/eq}, is rotated about the x-axis, find the area of the resulting surface.

## Surface Area of the Object:

In the given problem we have used the following formula to find the surface area of the object that is found by the rotation of the given 2 D function graph about the x-axis. The formula is {eq}S.A.=\int _a^b 2\pi y\sqrt{dx^{2}+dy^{2}} {/eq} This formula is only used if the axis of rotation is x-axis.

## Answer and Explanation:

The figure above shows the graph of {eq}\displaystyle y=e^{-4x} {/eq}

To find the surface area, we have taken a disk of radius...

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