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Stewart
Evaluate \(\iint_R x+2y \,\mathrm{d}A\) where \(R\) is the region in the \(xy\)-plane bounded by the parabolas \(y=2x^2\) and \(y=1+x^2.\) -
Stewart
Compute the volume of the solid that lies under the paraboloid \(z = x^2+y^2\) and above the region \(R\) in the \(xy\)-plane bounded by the line \(y=2x\) and the parabola \(y=x^2.\) -
Stewart
Compute the volume of the tetrahedron bounded by the planes \(x+2y+z = 2\) and \(x=2y\) and \(x=0\) and \(z=0.\) -
Stewart
Evaluate the iterated integral \(\int_0^1\int_x^1 \sin\big(y^2\big) \,\mathrm{d}y\,\mathrm{d}x.\) -
Dawkins
Compute the values of the following integrals on the indicated regions.\(\displaystyle \iint\limits_R \mathrm{e}^{\frac{x}{y}} \,\mathrm{d}A \quad\text{for } R = \big\{(x,y) \mid 1\leq y \leq 2, y\leq x \leq y^3\big\}\)\(\displaystyle \iint\limits_R 4xy - y^3 \,\mathrm{d}A\) for \(R\) bounded by \(y = \sqrt{x}\) and \(y=x^3\)\(\displaystyle \iint\limits_R 6x^2 - 40y \,\mathrm{d}A\) where \(R\) is the triangle with vertices \((0,3)\) and \((1,1)\) and \((5,3)\) -
Review
What is the area of the region bounded by a single “petal” of the rose curve \(r = \cos(5\theta)\) plotted in polar coordinates?