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. The part of the surface that lies above the disk x2 + y2 ≤ 81

A(s) = 255.8857

Step-by-step explanation:

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. The part of the surface z = e^-x^2-y^2 that lies above the disk x2 + y2 ≤ 81.

Given that:

By applying rule; the partial derivatives with respect to x and y

The integral over the general region D with respect to x and y is :

By relating the equation to cylindrical coordinates

The bounds for integration for the circle within the cylinder is r =9

Using integral calculator to estimate the  integral,we have:

A(s) = 255.8857

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,