Evaluate the double integral over the given region $R$ .
$\iint_{R} (27 y^{2} - 10 x) d A R : 0 \leq x \leq 3, 0 \leq y \leq 2$
$\iint_{R} (27 y^{2} - 10 x) d A =$

Answer

Expert–verified

Hide Steps

Answer

The final result of the double integral over the given region is $126$ .

Steps

Step 1 ：The given problem is a double integral over a rectangular region. The limits of integration for x and y are given. We can solve this problem by first integrating the function with respect to x, then integrating the result with respect to y.

Step 2 ：First, we integrate the function $- 10 x + 27 y^{2}$ with respect to x, keeping y as a constant. The limits of x are from 0 to 3.

Step 3 ：The result of the first integration is $81 y^{2} - 45$ .

Step 4 ：Next, we integrate this result with respect to y. The limits of y are from 0 to 2.

Step 5 ：The final result of the double integral over the given region is $126$ .

Evaluate the double integral over the given region R.∬R(27y2−10x)dAR:0≤x≤3,0≤y≤2∬R(27y2−10x)dA=

Answer

Popular Problems

Evaluate the double integral over the given region $R$ .
$\iint_{R} (27 y^{2} - 10 x) d A R : 0 \leq x \leq 3, 0 \leq y \leq 2$
$\iint_{R} (27 y^{2} - 10 x) d A =$