• Stewart

  Evaluate \(\iint_R 3x+4y^2 \,\mathrm{d}A\) where \(R\) is the region in the upper half-plane bound by the circles \(x^2+y^2=1\) and \(x^2+y^2=4.\)

• Stewart

  Evaluate the double integral \(\int_{-1}^{1}\int_{0}^{\sqrt{1-x^2}} x^2+y^2 \,\mathrm{d}y\,\mathrm{d}x\,.\)

• Stewart

  Calculate the volume of the solid that lies under the paraboloid \(z=x^2+y^2,\) above the \(xy\)-plane, inside the cylinder \(x^2+y^2=2x.\)

• Review

  Calculate the coordinates of the centroid of the region bounded by the curves \(x+y=2\) and \(y=x^3\) and \(y=0.\)

• Review

  Calculate the exact length of the graph of \(f(x) = \ln(\cos(x))\) between the points where \(x = 0\) and \(x = \frac{\pi}{3}.\)

• Review

  Suppose that the average height of women in the US is 5’4” with a standard deviation of 2.5”. Assuming that women’s heights are normally distributed this corresponds to the probability density function (PDF) \[f(x) = \frac{1}{2.5\sqrt{2\pi}}\mathrm{e}^{-\frac{1}{2}\big(\frac{x-64}{2.5}\big)^2}.\] Use this to approximate the percentage of women in the US who are taller than 6’.