b Under the assumption in a amend the integral so that the statement is correct

# B under the assumption in a amend the integral so

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(b)Under the assumption in (a), amend the integral so that the statement is correct.
P. 11 4.Use the substitution u= a2/3x2/3to find the area of the surface generated when the upper half of the astroid x2/3+ y2/3= a2/3is revolved about the x-axis. 5.Show that the surface area of the torus generated by revolving the circle x2+ (ya)2= r2, where 0 < r< a, about the x-axis is 4π2ar. 6.Show that the surface area of the zone obtained by slicing a sphere of radius rwith two vertical planes hunits apart is independent of the location of the cutting planes. 7.Let fbe differentiable on [a, b] and suppose that g(x) = f(cx), where c> 0. When the curve y= f(x) on [a, b] is revolved about the x-axis, the resulting surface area is A. Evaluate the integral cbcadxxgcxg//22)()(in terms of Aand c. 8.Suppose fis positive and differentiable on [a, b]. Let Lbe the arc length of fon [a, b] and Sbe the surface area generated by revolving the graph of fon [a, b] about the x-axis. Show that the surface area generated by revolving the graph of y= f(x) + C, where C> 0, about the x-axis is the sum of Sand the surface area of a right circular cylinder of radius Cand height L.
P. 12 Integration by Parts Integration by Parts: vduuvudv1.Evaluate the following integrals. 2dxxexdxxxx211sin(i)dxx)cos(ln2.Show that xxdxdcos112tan. Hence, evaluate dxxxxcos1sin. 3.Show that for n1, Cnxnxxdxxnn11ln1ln1. Hence, evaluate 212lnexdxx. 4.Prove the integration formula Cbxabxbbaebxdxeaxax)cossin(cos22and hence evaluate the following integrals. (a)xdxexcos(b)xdxex2cos3
P. 13 5.Prove the integration formula Cbxbbxabaebxdxeaxax)cossin(sin22and hence evaluate the following integrals. (a)xdxex4sin(b)xdxex6sin26.Derive the following reduction formulas. naexdxexaxnaxnaxn1for a≠ 0naaxxaxdxxnnnsinsincos1for a≠ 0naaxxaxdxxnnncoscossin1for a≠ 0
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