calculus

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could some body please check this for me?

1. find the exact coordinates of the centroid of the region bounded by y-x^2, the x axis, the y axis, and the line x=1?

I said the answer was ((3/4), (3/10))

2. Find the exact coordinates of the centroid of the region to the right of the y axis between y=2e^(-2x) and the x axis. Note this region is unbounded but has a finite area.

I said the answer was ((1/2), (1/2))

THANK YOU

  • calculus -

    1. Do you mean y = x^2? You wrote y-x^2. That is not a curve.

    If you mean y = x^2, the area-weighted mean value of y is
    [integral of y(y/2)dx] divided by 1/3
    x = 0 to 1

    = 3/10

    The area-weighted mean value of x is
    integral of y*x dx divided by 1/3
    x = 0 to 1

    = integral of x^3 dx divided by 1/3
    x = 0 to 1

    = 3/4

    The division by 1/3 is normalizing by the area of the region. I agree with your answers. If you followed the same procedure for problem 2, your answers to that one are also correct.

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