6. The base of a solid sitting on thexy-plane is the region enclosed by the curvesx=-π4,y= 2 sinxandy= 2 cosxover the interval-π4≤x≤π4.Suppose that each cross section of the solidperpendicular to thex-axis is an equilateral triangle (i.e.all sides have equal length).Find thevolume of the solid.xy√3π3√3π5√3π7√3π9√3π(a)2(b)2(c)2(d)2(e)2
7. The region enclosed by the graph of the functiony= 2x2and the liney= 16 is rotated about they-axis to generate a solid of revolution. Find the average value of the cross section areas of the solidwhich are perpendicular to they-axis.
8. Letfbe a positive differentiable function satisfyingf(0) = 1,f(1) = 2,f′(0) = 2,f′(1) = 3.Evaluate the integralintegraldisplay10f′(x) ln(f(x))dx.