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Math Help - Area Volume

  1. #1
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    Area Volume

    1. Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.


    2. Find the area of the region between and for .
    area =????

    3. Find the area of the region enclosed between and from to . Hint: Notice that this region consists of two parts.


    Please help and explains..Thanks
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  2. #2
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    Quote Originally Posted by Kayla_N View Post
    1. Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.


    2. Find the area of the region between and for .
    area =????

    3. Find the area of the region enclosed between and from to . Hint: Notice that this region consists of two parts.


    Please help and explains..Thanks
    1) If you graph the the two equations on a graphing device, you will notice that y = 5x is above y = 6x^2. Hence your integral will be with respect to x integrating (5x - 6x^2)dx between the two point of intersection. The intersection can be found by equation 6x^2 = 5x and solving for x.

    2) Use the same method from the previous question but now your limits are from 0 to 1 with respect to x. Remember you are subtracting two areas essentially, so the bottom function which has a smaller area beneath it should be subtracted from the top with a larger area. This technique is easy to employ by again, using a graphing device.

    3) Ill leave as an exercise to you hoping that the previous two have helped you

    Please message if you need further clarification
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  3. #3
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    Quote Originally Posted by Kayla_N View Post
    1. Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.


    2. Find the area of the region between and for .
    area =????

    3. Find the area of the region enclosed between and from to . Hint: Notice that this region consists of two parts.


    Please help and explains..Thanks

    So for number 1, i followed your instruction and graphed and solved for x. X= 0 and 5/6. Now how do i plug it in to find the area??
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  4. #4
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    Quote Originally Posted by Kayla_N View Post
    So for number 1, i followed your instruction and graphed and solved for x. X= 0 and 5/6. Now how do i plug it in to find the area??
    \int_0^{\frac{5}{6}} 5x \cdot dx - \int_0^{\frac{5}{6}} 6x^2 \cdot dx
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  5. #5
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    Quote Originally Posted by e^(i*pi) View Post
    \int_0^{\frac{5}{6}} 5x \cdot dx - \int_0^{\frac{5}{6}} 6x^2 \cdot dx
    There you go some one got there before me :P
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