Calculate the double integral. $$\iint _ { R } \left( 12 x ^ { 2 } y ^ { 3 } - 20 x ^ { 4 } \right) d A , R = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 4 \}$$
A) $310$
B) $240$
C) $290$
D) $270$
E) $250$

Question

Quizplus · Accepted Answer

The integral is evaluated as $\int_0^1 \int_0^4 (12x^2y^3 - 20x^4) \, dy \, dx$. First, integrate with respect to $y$, then with respect to $x$. The result is 240.

Calculate the Double Integral ∬R(12x2y3−20x4)dA,R={(x,y)∣0≤x≤1,0≤y≤4}\iint _ { R } \left( 12 x ^ { 2 } y ^ { 3 } - 20 x ^ { 4 } \right) d A , R = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 4 \}∬R​(12x2y3−20x4)dA,R={(x,y)∣0≤x≤1,0≤y≤4}

Calculate the Double Integral $\iint _ { R } \left( 12 x ^ { 2 } y ^ { 3 } - 20 x ^ { 4 } \right) d A , R = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 4 \}$