Explore BrainMass

Explore BrainMass

    Volume of Solid by Double Integration

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Find the volume of the solid in the first octant bounded by the surfaces of z = 1 - y^2, y = 2, and x = 3.

    © BrainMass Inc. brainmass.com June 7, 2023, 10:38 pm ad1c9bdddf

    Solution Preview

    Given a function y = f(x) of a single variable x, we know that the definite integral:

    Integral { f(x) dx, x = a to b }

    gives the area under the curve y = f(x), between the portions x = a and x = b.

    Similarly, for a function z = f(x, y) of two variables x and y, we can use double integration to find the volume under the surface defined by z = f(x, y) over a rectangular portion of the x-y plane (this rectangular region being defined by the limits of integration).

    Here, the function is:

    z = 1 - ...

    Solution Summary

    Finding the volume of a solid region by using double integration is a standard problem in multi-variable calculus. This solution demonstrates the method by means of an example worked out in detail. A diagram is included showing the region of integration (attached as a PNG image). Additionally, this solution includes references for further reading on the theory behind this question.


    Free BrainMass Quizzes

    • Multiplying Complex Numbers

      This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

    • Graphs and Functions

      This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

    • Probability Quiz

      Some questions on probability

    • Solving quadratic inequalities

      This quiz test you on how well you are familiar with solving quadratic inequalities.

    • Exponential Expressions

      In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

    View More Free Quizzes