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Math Help - Find Area of the Region

  1. #1
    Senior Member nycmath's Avatar
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    Find Area of the Region

    Find the area of the region bounded by the graphs of the equations.

    y = x^3 + x, x = 2, y = 0.

    I know how to set up the integral to solve this problem. Previous questions gave two values for x that became the upper and lower limits of integration. In this question, only one x value is given. What are the limits of integration here? I can then complete the problem.
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  2. #2
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    Re: Find Area of the Region

    Quote Originally Posted by nycmath View Post
    Find the area of the region bounded by the graphs of the equations.

    y = x^3 + x, x = 2, y = 0.

    I know how to set up the integral to solve this problem. Previous questions gave two values for x that became the upper and lower limits of integration. In this question, only one x value is given. What are the limits of integration here? I can then complete the problem.
    \int_0^2 {({x^3} + x)dx}
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  3. #3
    Senior Member nycmath's Avatar
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    Re: Find Area of the Region

    That was my second choice for x.
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    Re: Find Area of the Region

    Quote Originally Posted by nycmath View Post
    That was my second choice for x.
    Well, that is the only bounded area.
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  5. #5
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    Re: Find Area of the Region

    Hello, nycmath!

    Did you make a sketch?


    Find the area of the region bounded by the graphs of the equations.
    . . y = x^3 + x, .x = 2, .y = 0.

    What are the limits of integration here?

    The graph looks like this:

    Code:
                  |
                  |      *
                  |      '
                  |     *'
                  |   .*:'
                  | .*:::'
          - - - - * - - -+- -
               *  |      2
             *    |
            *     |
                  |
           *      |
                  |
    Can you see the limits now?
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  6. #6
    Senior Member nycmath's Avatar
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    Re: Find Area of the Region

    Thanks everyone.
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  7. #7
    Senior Member nycmath's Avatar
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    Re: Find Area of the Region

    Quote Originally Posted by Soroban View Post
    Hello, nycmath!

    Did you make a sketch?



    The graph looks like this:

    Code:
                  |
                  |      *
                  |      '
                  |     *'
                  |   .*:'
                  | .*:::'
          - - - - * - - -+- -
               *  |      2
             *    |
            *     |
                  |
           *      |
                  |
    Can you see the limits now?
    The limits are [0,2]. Soroban, check your inbox.
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