Parametric Equations and integrals that represent volumes

In summary, parametric equations are a set of equations that express quantities as functions of parameters. They are commonly used to describe motion and simplify calculations involving multiple variables. Integrals are mathematical concepts used to find the sum of infinitesimal parts of a function over an interval. Parametric equations and integrals are related in that parametric equations can be used to represent the boundaries of three-dimensional shapes, which can then be integrated to find their volume. To find the volume of a shape using parametric equations and integrals, one must first find the parametric equations for the shape's boundaries, set up an integral using these equations, and then solve for the volume.
  • #1
peterpam89
5
0

Homework Statement



A surface S is formed by rotating a quarter ellipse C about the X-axis. Write an integral that represents the volume enclosed by S. the ellipse is represented by two points, (2,1) at which t= pi/2, and (4,0) at which t=0.

Homework Equations



Ellipse w/radii a,b, in x,y: x= x subscript 0 + a cos (t), y = y subscript 0 + b sin (t)
Cartesian equation of ellipse.

The Attempt at a Solution



Eek. I don't really know where to even start with this problem... any ideas?
 
Physics news on Phys.org
  • #2
You could try x(t)=2+2*cost and y(t)=sint
 

Related to Parametric Equations and integrals that represent volumes

What are parametric equations?

Parametric equations are a set of equations that express a set of quantities as functions of one or more independent variables, known as parameters. In other words, the variables in a parametric equation are dependent on one or more parameters.

What is the purpose of using parametric equations?

Parametric equations are often used to describe the motion of objects in space or to represent complex curves and surfaces. They can also be used to simplify calculations and solve problems involving multiple variables.

What is an integral?

An integral is a mathematical concept that represents the sum of infinitesimal parts of a function over a given interval. It is used to calculate the area under a curve or the volume of a three-dimensional shape.

How are parametric equations and integrals related?

Parametric equations can be used to represent the boundaries of a three-dimensional shape, which can then be integrated to find its volume. For example, the parametric equations for a sphere can be integrated to find its volume.

What is the process for using parametric equations and integrals to find volume?

To find the volume of a three-dimensional shape using parametric equations and integrals, you will need to first find the parametric equations that represent the boundaries of the shape. Then, you can use these equations to set up an integral that will calculate the volume. Finally, you can solve the integral to find the volume of the shape.

Similar threads

Correct Parametrization for Calculating Area of a Tube?
    • Calculus and Beyond Homework Help
Replies
2
Views
782
Graph the Cartesian equation: x = 2 sin t, y = 4 cos t
    • Calculus and Beyond Homework Help
Replies
1
Views
8K
Prove that PA=2BP in the problem involving parametric equations
    • Calculus and Beyond Homework Help
Replies
2
Views
649
Calculating crossproduct integral, Parametrization
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Finding the largest ellipse that will fit in a polygon
    • Calculus and Beyond Homework Help
Replies
4
Views
2K
Volume of Static Solid Using Cross-Sectional Area (Integration)
    • Calculus and Beyond Homework Help
Replies
2
Views
300
Determine limits of integration in double integral change of variables
    • Calculus and Beyond Homework Help
Replies
2
Views
496
Solve the given parametric equation
    • Calculus and Beyond Homework Help
Replies
3
Views
973
Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
    • Calculus and Beyond Homework Help
Replies
7
Views
866
How to draw phase portrait for 2x2 nonlinear system of DE?
    • Calculus and Beyond Homework Help
Replies
1
Views
372

Hot Threads

Recent Insights

Back
Top