math

let R be the region bounded by the graphs of y = sin(pie times x) and y = x^3 - 4.

a) find the area of R

b) the horizontal line y = -2 splits the region R into parts. write but do not evaluate an integral expression for the area of the part of R that is below this horizontal line.

c) The region R is the base of a solid. For this solid, each cross section perpendicular to x-axis is a square. Find the volume of this solid.

d) the region R models the surface of a small pond. At all points in R at a distance x from the y-axis, the depth of the water is given by h(x)=3-x. find the volume of the water in the pound.

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  1. y = sin (pi x) has to be between -1 and +1 It seems to me it only intercepts the y = x^3 -4 curve once, at around x = 1.45.

    Therefore I don't see how one can define a closed region R between the curves.

    Something is fishy here

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  2. I also noticed that you had posted this same question twice so far, and just like "drwls", I was confused by what "region R" you were talking about.

    I was going to assume that the region was between the sine curve, the cubic and the y-axis, but that meant solving
    sinx = x^3 - 4
    which would be a major undertaking.

    If that is the case, and once that intersection point between y = sinx and y = x^3-4 has been found, the question would not be that difficult.
    Please clarify and one of us will attempt to help you out.

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  3. I agree with Reiny, but believe he meant to write sin (pi*x) instead of sin x for one of the y functions

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