Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral.
13. The part of the surface z = 1/(1 + x2 + y2) that lies above the disk x2 + y2 ≤ 1
To find: The area of given surface correct to four decimal places by using integrating calculator.
The function is the part of the surface .
The region D lies above the disk .
The surface area with equation , where and are continuous, is .
Here, D is the given region.
If is a polar rectangle R given by , where , then, (1)
If is the function of and is the function of then,
Convert the given problems into the polar coordinates to make the problem easier. By the given the conditions, it is observed that, r varies from 0 to 1 and varies from 0 to .
The partial derivatives and are,
Then, by the equation (1), the area of surface is given by,
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