Given a curve having an equation of y2=4x. a) Compute the area bounded by the curve and the line y=4 and x=0. b) How far is the centroid of the curve bounded by the line y=4 and x=0 from the x-axis. c) What is the volume generated by this curve if it is revolved about the x-axis.

Question

Given a curve having an equation of y2=4x.  a) Compute the area bounded by the curve and the line y=4 and x=0.  b) How far is the centroid of the curve bounded by the line y=4 and x=0 from the x-axis.  c) What is the volume generated by this curve if it is revolved about the x-axis.

turtletalk75 · Accepted Answer

Given: - y2=4x To Find: - Area bounded by the curve y=4,x=0  Area =∫x=ax=b∫y=f1(x)y=f2(x)dy dx ∫04∫2x()4dy dx=∫04(4−2x())dx =[4x−2x3232]{0}4=[4x−4x323]{0}4 =(4(4)−43432)−(0) =16−323=163

Deufemiak7 · Accepted Answer

b) To Find: - How For centroid of  centroid  X-axis  i.e. we need to find y coordinute  of centroid  y=1Area∫x=ax=b12((f(x)2)−(g(x)2)dx  =1163∫0412[42−(2x())2]dx  =332∫04(16−4x)dx  =3×432∫04(4−x)dx  =38[4x−x22]=38(8)=3   Centroid of curve is 3 from  x-axis

karton · Accepted Answer

c) To Find: - Value generated by come f revolved about x-axis: Volume of Solid revolved about the x-axis is given by V=π∫x=ax=b[f(x)2]−[g(x)2]()dx whose y=f(x) is upper come f y=g(x) lower curve. ∴V=π∫04[42−x22]dx=π∫04(16−4x)dx=4π∫04(4−x)dx=4π[4x−x22]04=4π[16−162]=4π(8)=32π

Given a curve having an equation of y^{2} = 4x. a)

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