Practice: Double Integrals over General Regions (2)

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Double Integration (rectangular)

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Evaluate ∫D∫(6x2−40y)dA \displaystyle\int_D\int\Bigg(6x^2-40y\Bigg)dA~∫D​∫(6x2−40y)dA where D is the triangle with vertices (0, 3), (1, 1), and (5, 3). 

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More Double Integration (rectangular) Questions:

Practice: Changing the order of integration

Evaluate
∫01∫x1ey2dydx\int_0^1\int_x^1e^{y^2}dydx∫01​∫x1​ey2dydx

Practice: Double Integrals over General Regions (2)

Evaluate ∫D∫(6x2−40y)dA \displaystyle\int_D\int\Bigg(6x^2-40y\Bigg)dA~∫D​∫(6x2−40y)dA where D is the triangle with vertices (0, 3), (1, 1), and (5, 3). 

Practice: Double integration

Compute ∬Dln⁡(ln⁡(x))dA\displaystyle \iint_D\ln(\ln(x))dA∬D​ln(ln(x))dA where DDD is the region bounded by y=0y = 0y=0, xy=1xy = 1xy=1, x=ex=ex=e, and x=e2x=e^2x=e2.