Question

2. Evaluate the double integral Z Z R e ^(x^ 2+y ^2) dA where R is...

2. Evaluate the double integral Z Z R e ^(x^ 2+y ^2) dA where R is the semicircular region bounded by x ≥ 0 and x^2 + y^2 ≤ 4.

3. Find the volume of the region that is bounded above by the sphere x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 + y^2 .

4. Evaluate the integral Z Z R (12x^ 2 )(y^3) dA, where R is the triangle with vertices (0, 0), (1, 1) and (2, 0).

ZZ means double integral. All x's are variables. Thank you!

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