What is the integral of the constant function f(x,y)=5 over the rectangle [−2,3]×[2,4]?

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Alix Ortiz · Accepted Answer

Step 1 Integration of a function gives the result as the area covered by the function with an appropriate axis. INtegrals are of two types, definite and indefinite integrals. Definite integrals are defined for a limit of variable from a lower limit to an upper limit. This is represented by the expression:- I=∫abf(x)dx =F(b)−F(a) Here, F(x) is the anti-derivative of the function f(x). Step 2 The value of the definite integral is constructed by using the limits of x from -2 to 2, and the limts of y from 3 to 4 as I=∫34∫−22f(x,y)dxdy. This integral is calculated as follows:- I=∫34∫−22f(x,y)dxdy =∫34∫−225dxdy =5∫34∫−22dxdy =5∫34[x]−22dy =5∫34(2−(−2))dy =20∫34dy =20[y]34=20

What is the integral of the constant function f (x, y) = 5 over the rectangle [-2,3]\times[2,4]?

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