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Math Help - Area under the curve!

  1. #1
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    Area under the curve!

    Hello everyone.
    I would really appreciate it if you helped me out with this question.

    Find the are of the region shaded in the diagram.

    The equation of the curve is y=3x^8+5

    I found the x points as -1 and 1 but i cant seem to get further.

    Thank you.
    Attached Thumbnails Attached Thumbnails Area under the curve!-maths2.jpg  
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  2. #2
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    y1=3x^8+5
    y2 = 8

    Area of the shaded region = Integration(y2-y1)dx over -1 to 1 will give you the area. This integration is very straight forward.
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  3. #3
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    could you please make it more clear.
    y2=8?
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  4. #4
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    y2 = 8 is the straight line in your diagram below which the shaded region is shown.
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  5. #5
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    Quote Originally Posted by Oasis1993 View Post
    Hello everyone.
    I would really appreciate it if you helped me out with this question.

    Find the are of the region shaded in the diagram.

    The equation of the curve is y=3x^8+5

    I found the x points as -1 and 1 but i cant seem to get further.

    Thank you.
    the method is the same as the other problem you posted ...

    \int_{-1}^1 8 - (3x^8+5) \, dx

    or, using symmetry, ...

    2 \int_0^1 8 - (3x^8+5) \, dx
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