Use adequate parentheses.pious&peevish said:Homework Statement
Find the surface area of the surface defined by:
z = (2/3)(x^(3/2) + y^(3/2)), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
Homework Equations
SA = ∫∫ √(fx)^2 + (fy)^2 + 1 dA
The Attempt at a Solution
Solved for the partial derivatives and plugged them into the formula, but got a really messy answer in the end. I think I was supposed to do a change of variables somewhere but I'm not sure how...
pious&peevish said:Yes, sorry - I meant ∫∫ √((fx)^2 + (fy)^2 + 1) dA .
I had √(x) for ∂f/∂x and √(y) for ∂f/∂y.
Double integration is a mathematical technique used to find the total area under a curve by integrating twice. It is commonly used in calculus and physics to solve problems involving two variables.
Double integration can be used to find the surface area of a three-dimensional shape by integrating twice in the x and y directions. This method is often used to find the surface area of curved and irregular shapes.
In single integration, the area under a curve is found by integrating in one direction. In double integration, the area under a surface is found by integrating in two directions. Double integration is more complex and is used for finding the surface area of three-dimensional shapes.
Double integration has many practical applications, such as calculating the volume of a water tank, determining the amount of paint needed to cover a curved surface, and finding the surface area of a 3D object in engineering and architecture.
One common mistake is integrating in the wrong direction or using the wrong limits of integration. It is also important to correctly set up the integrals for each variable and to carefully evaluate the integrals to avoid errors. Another mistake is forgetting to include all necessary variables in the integrand.