Question

For the integral ∫ from -3 to 0, ∫ from -√(25-x²) to 0 of 3xy dy dx, sketch the region of integration and evaluate the integral. Your sketch should be approximately the same as one

Answer 1

To evaluate the integral, sketch the region of integration and then set up and integrate the double integral using the given function and limits of integration.

Step-by-step explanation:

To evaluate the given integral, we first need to sketch the region of integration. The integral is a double integral, with the outer integral being from -3 to 0 and the inner integral being from -√(25-x²) to 0. The region of integration represents the area under the curve y=√(25-x²) and above the line y=0 within the given limits.

Once we have sketched the region of integration, we can evaluate the integral. Using the given function 3xy and the limits of integration, we can set up the double integral and then integrate it step by step. The final result will give us the value of the integral.