Double Integrations on Plane

Practice Questions

Multivariable Calculus › Double Integrations on Plane

Questions

10

1

Evaluate $\int \int_R 3x+2y \ dA$ , where is the trapezoidal region with vertices given by , , $(\frac{5}{2}, \frac{5}{2})$ , and $(\frac{5}{2}, -\frac{5}{2})$ ,

using the transformation , and .

2

Convert the following into spherical coordinates.

$x=\sin(t)$

$y=\cos(t)$

3

Calculate the following Integral.

$\int_{0}^{1}\int_{x}^{x^2} xy^2 dydx$

4

Convert the following into spherical coordinates.

$x=\sin(t)$

$y=\cos(t)$

5

Evaluate $\int \int_R 3x+2y \ dA$ , where is the trapezoidal region with vertices given by , , $(\frac{5}{2}, \frac{5}{2})$ , and $(\frac{5}{2}, -\frac{5}{2})$ ,

using the transformation , and .

6

Calculate the following Integral.

$\int_{0}^{1}\int_{x}^{x^2} xy^2 dydx$

7

Calculate the following Integral.

$\int_{0}^{1}\int_{x}^{x^2} xy^2 dydx$

8

Calculate the following Integral.

$\int_{0}^{1}\int_{x}^{x^2} xy^2 dydx$

9

Convert the following into spherical coordinates.

$x=\sin(t)$

$y=\cos(t)$

10

Convert the following into spherical coordinates.

$x=\sin(t)$

$y=\cos(t)$

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