Double Integral Problem/ Surface Area of parametric surface

Therefore, the solution involves solving the inner integral first and then plugging that into the outer integral.
  • #1
Dizzy1
4
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Hi I'm doing a surface area problem with a parametric surface and I got the cross product but I can't figure out the double integral.

I found the solution online but with no explanation, so can someone explain how to solve this integral:

View attachment 2449

thank you!
 

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  • #2
Dizzy said:
Hi I'm doing a surface area problem with a parametric surface and I got the cross product but I can't figure out the double integral.

I found the solution online but with no explanation, so can someone explain how to solve this integral:

View attachment 2449

thank you!

Because the inner integral is just a number you can immediately do the outer integral so:

\(\displaystyle \int_0^{\pi}\ \int_0^1\sqrt{1+u^2}du\ dv=\pi \int_0^1\sqrt{1+u^2}du\)

.
 

FAQ: Double Integral Problem/ Surface Area of parametric surface

What is a double integral problem?

A double integral problem is a type of mathematical problem that involves finding the area under a 2-dimensional function over a specified region in a coordinate plane. It is essentially a 2-dimensional version of a single integral, where the function is integrated over a single variable.

How is a double integral problem solved?

A double integral problem is solved by breaking the region into small, rectangular sub-regions and approximating the area under the function in each sub-region. These small areas are then added together to get an overall approximation of the total area under the function.

What is a parametric surface?

A parametric surface is a surface in 3-dimensional space that is defined by a set of 3 equations, each containing 2 parameters. These parameters act as variables that determine the coordinates of points on the surface. Parametric surfaces are often used to model and describe complex 3-dimensional shapes.

How do you find the surface area of a parametric surface?

The surface area of a parametric surface can be found by using a double integral to integrate the square root of the sum of the squared partial derivatives of each parameter with respect to the other two parameters. This integral is taken over a specified region on the surface.

What are some real-life applications of double integrals and parametric surfaces?

Double integrals and parametric surfaces are used in many fields, including physics, engineering, and computer graphics. Some real-life applications include calculating the volume of a 3-dimensional object, finding the average value of a function over a region, and creating 3-dimensional computer models of complex shapes and surfaces.

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