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

avissidep 2021-06-01 Answered

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

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Expert Answer

Alix Ortiz
Answered 2021-06-02 Author has 109 answers

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=3422f(x,y)dxdy. This integral is calculated as follows:-
I=3422f(x,y)dxdy
=34225dxdy
=53422dxdy
=534[x]22dy
=534(2(2))dy
=2034dy
=20[y]34=20

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