# Let #b > a > 0# be constants. Find the area of the surface generated by revolving the circle #(x − b)^2 + y^2 = a^2# about the y-axis?

##
Let #b > a > 0# be constants. Find the area of the surface generated by revolving the circle #(x − b)^2 + y^2 = a^2# about the y-axis?

Let

By signing up, you agree to our Terms of Service and Privacy Policy

To find the area of the surface generated by revolving the circle ((x - b)^2 + y^2 = a^2) about the y-axis, we can use the formula for the surface area of revolution:

[ A = 2\pi \int_{c}^{d} y \sqrt{1 + \left(\frac{dx}{dy}\right)^2} , dy ]

First, solve the equation of the circle for (x) to get (x = \pm \sqrt{a^2 - y^2} + b).

Then, differentiate (x) with respect to (y) to find (\frac{dx}{dy}).

Next, integrate (y \sqrt{1 + \left(\frac{dx}{dy}\right)^2}) with respect to (y) from (c) to (d), where (c) and (d) are the (y)-coordinates of the points of intersection of the circle and the y-axis.

Finally, multiply the result by (2\pi) to get the total surface area.

Please note that the limits of integration and other details would need to be determined based on the specific circle and the points of intersection with the y-axis.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Find the area between the curve # y = e^(2x) # y = 0 from x = 1 to 3 ?
- How to find the area of the region bounded by the curves y = x^4 and y = 8x ?
- How do you find the area under the graph of #f(x)=x^2# on the interval #[-3,3]# ?
- How do you find the area under one half period of #y=2sin3x#?
- How do you find the area between #f(x)=2-1/2x# and #g(x)=2-sqrtx#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7