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Find the area of the surface generated by revolving the curve y = sqrt(2x - x²) about the x-axis.

a) 6.98
b) 8.14
c) 10.07
d) 12.53

User Asnad Atta
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1 Answer

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Final answer:

To find the area of the surface generated by revolving the curve y = sqrt(2x - x²) about the x-axis, we can use the formula for the surface area of a solid of revolution. This involves finding the limits of integration, substituting the values into the formula, and solving the integral using standard techniques.

Step-by-step explanation:

To find the area of the surface generated by revolving the curve y = sqrt(2x - x²) about the x-axis, we can use the formula for the surface area of a solid of revolution:

A = 2π∫[a,b] y(x)√(1 + (dy/dx)²) dx

In this case, the curve is y = sqrt(2x - x²), so we need to find the limits of integration a and b. We can do this by solving the equation 2x - x² = 0.

Solving for x:

2x - x² = 0

x(2 - x) = 0

x = 0 or x = 2

So the limits of integration are a = 0 and b = 2. Now we can substitute these values into the formula and calculate the area:

A = 2π∫[0,2] sqrt(2x - x²)√(1 + (d(sqrt(2x - x²))/dx)²) dx

This integral can be solved using standard integration techniques, and the result will give us the area of the surface generated by revolving the curve about the x-axis.

User Golam Sorwar
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