A region R is bounded by y = Squareroot x and y = x^6. Set up the integral to fi

Question

A region R is bounded by y = Squareroot x and y = x^6. Set up the integral to find the volume V of the solid formed by rotating R around the x-axis and then find the volume. Let f(x) = 7x + Squarerootx + 50. Choose the form of the largest interval on which f has an inverse and enter the value(s) of the endpoint(s) in the appropriate blanks. Then find (f^-1)'(0). Enter DNE in any unused answer blank. (-infinity, infinity) (-infinity, b)) (-infinity, b) (a, b) (a, b] [a, b) [a, b] (a, infinity) [a, infinity) a = b = (f^-1)'(0) =

Explanation / Answer

y =x , y =x6

x =x6

x=x12

x(x11-1)=0

x=0,x=1

volume of solid about x axis by washer metod v =[0 to 1]((x)2 - (x6)2) dx

v =[0 to 1](x - x12) dx

v =[0 to 1]((1/2)x2 - (1/13)x13)

v=((1/2)12 - (1/13)113) -((1/2)02 - (1/13)013)

v=((1/2) - (1/13))

v=(11/26)

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