Evaluate the integral.
-$$\int _ { - 3 } ^ { 10 } \int _ { - 10 } ^ { - 4 } 5 x d y d x$$
A) - 2730
B) - 2535
C) - 1170
D) 1365

Question

Quizplus · Accepted Answer

The integral simplifies as follows: First, integrate with respect to $y$, treating $x$ as a constant. Since there are no $y$ terms in the integrand, the integral of $5x$ with respect to $y$ over the interval $[-10, -4]$ is $5x(y)\Big|_{-10}^{-4} = 5x(-4 + 10) = 30x$. Next, integrate $30x$ with respect to $x$ over the interval $[-3, 10]$: $\int_{-3}^{10} 30x dx = 15x^2\Big|_{-3}^{10} = 15(10^2) - 15(-3)^2 = 1500 - 135 = 1365$.

Evaluate the Integral ∫−310∫−10−45xdydx\int _ { - 3 } ^ { 10 } \int _ { - 10 } ^ { - 4 } 5 x d y d x∫−310​∫−10−4​5xdydx

Evaluate the Integral $\int _ { - 3 } ^ { 10 } \int _ { - 10 } ^ { - 4 } 5 x d y d x$