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Use the region $R$ with the indicated boundaries to evaluate each double integral.$$\iint_{R}(2 x+6 y) d y d x ; \quad 2 \leq x \leq 4,2 \leq y \leq 3 x$$
Use the region $R$ with the indicated boundaries to evaluate each double integral.$$\iint_{R}\left(4-4 x^{2}\right) d y d x ; 0 \leq x \leq 1,0 \leq y \leq 2-2 x$$
Use the region $R$ with the indicated boundaries to evaluate each double integral.$$\iint_{R} \frac{1}{x} d y d x ; \quad 1 \leq x \leq 2,0 \leq y \leq x-1$$
Use the region $R$ with the indicated boundaries to evaluate each double integral.$$\iint_{R} e^{x / y^{2}} d x d y ; \quad 1 \leq y \leq 2,0 \leq x \leq y^{2}$$
Use the region $R$ with the indicated boundaries to evaluate each double integral.$$\iint_{R}\left(x^{2}-y\right) d y d x ;-1 \leq x \leq 1,-x^{2} \leq y \leq x^{2}$$
Use the region $R$ with the indicated boundaries to evaluate each double integral.$$\iint_{R}(x+14 y) d y d x ; 0 \leq x \leq 5,0 \leq y \leq 5-x$$
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