carl123 said:If R = [−3, 1] × [−2, 0], Use a Riemann sum with m = 4, n = 2 to estimate the value of ∫∫R(y2 − 2x2) dA. Take the sample points to be the upper left corners of the squares.
So far,
I found the indefinite integral of the function to be y3/3 - 2x3/3
Not sure where to go from here
A Reimann sum is a method used to approximate the value of a definite integral by dividing the interval into smaller subintervals and computing the areas of rectangles that fit under the curve.
In a double integral, the interval is divided into smaller subintervals in both the x and y directions. The areas of the rectangles formed in each subinterval are then added together to approximate the value of the double integral.
Using a Reimann sum allows for a more accurate estimation of the value of a double integral compared to other methods. It also allows for the use of smaller subintervals, resulting in a more precise approximation.
The number of subintervals used in a Reimann sum depends on the desired level of accuracy. Generally, the more subintervals used, the more accurate the estimation will be. However, it is important to balance this with the computational cost of using a larger number of subintervals.
Yes, a Reimann sum can be used to estimate the value of any double integral, as long as the interval is divided into small enough subintervals and the rectangles are accurately computed. However, as the complexity of the function increases, a larger number of subintervals may be needed for a more accurate estimation.