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Stewart
Compute the values of the following integrals on the indicated rectangles.\(\displaystyle \iint\limits_R x-3y^2 \,\mathrm{d}A \quad\text{for } R = \{(x,y) \mid 0\leq x\leq 2, 1\leq y\leq 2\}\)\(\displaystyle \iint\limits_R y\sin(xy) \,\mathrm{d}A \quad\text{for } R = [1,2]\times[0,\pi]\) -
Stewart
For \(R = \{(x,y) \mid -1\leq x \leq 1, -2\leq y\leq 2\}\) evaluate the integral \(\iint_R \sqrt{1-x^2} \,\mathrm{d}A.\) -
Stewart
Compute the volume of the solid \(S\) that is bounded by the elliptic paraboloid \(x^2+2y^2+z=16,\) the planes \(x=2\) and \(y=2,\) and the coordinate planes. -
Dawkins
Compute the values of the following integrals on the indicated rectangles.\(\displaystyle \iint\limits_R 6xy^2 \,\mathrm{d}A \quad\text{for } R = [2,4]\times[1,2]\)\(\displaystyle \iint\limits_R 2x-4y^3 \,\mathrm{d}A \quad\text{for } R = [-5,4]\times[0,3]\)\(\displaystyle \iint\limits_R \frac{1}{(2x+3y)^2} \,\mathrm{d}A \quad\text{for } R = [0,1]\times[1,2]\)\(\displaystyle \iint\limits_R x\mathrm{e}^{xy} \,\mathrm{d}A \quad\text{for } R = [-1,2]\times[0,1]\) -
Review
What is the area of the region in the \(xy\)-plane bounded by the curves \(y^2=x\) and \(y=\mathrm{e}^x\) and \(y=2-x\) and the \(y\)-axis?