Chapter 2, Problem 45RE

Calculate the area of the segment cut from the curve y=x(3−x) by the line y=x. Also, sketch the graph.

y =  x2+3     y=11-x2 Find the area between the curves

x= y^2 - 4y   x= y-y^2   find the area

Give Solution

Number 6

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Drinking juice A glass has circular cross sections that taper (linearly) from a radius of 5 cm at the top of the glass to a radius of 4 cm at the bottom. The glass is 15 cm high and full of orange juice. How much work is required to drink all the juice through a straw if your mouth is 5 cm above the top of the glass? Assume the density of orange juice equals the density of water.

A curve is such that the area bounded between the curve, the y-axis, the x-axis and the line parallel to the x-axis passing through P(x, y) is equal to x + y. Find the equation of the curve.