Question #253436

Find the volume generated by rotating the region bounded by line y=4 from x=1 to x=7, about the a. x-axis b. y-axis

Expert's answer

Consider a region that is bounded by two curves

"y=f(x)"

and

"y=g(x)"

between"x=a" and "x=b"

"(\nf\n(\nx\n)\n,\ng\n(\nx\n)\nf(x),g(x)" are continuous and non-negative on

the interval "[a,b]"

And "f(x)\\leq g(x)" )

The volume of the solid formed by revolving the region about the x-axis is

"V=\u03c0 \na\n\u222b\nb\n\u200b\t\n ([f(x)] \n2\n \u2212[g(x)] \n2\n )dx"

We have three curves:"y=x, y^2=4x" And x=1

The region that is bounded by them can be defined as a region that is bounded by"f(x)=2\\sqrt {x}"

Answer: the volume is"\\frac{5\\pi}{3}."

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