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vekshin1
2 years ago
6

Write one or more integrals using the order of integration dxdy equivalent to f(x, y) dydx​

Mathematics
1 answer:
stira [4]2 years ago
4 0

The lines y=\frac x2 and y=3-x meet when

\dfrac x2 = 3-x \implies \dfrac{3x}2 = 3 \implies x=2

at which point y=\frac22 = 1. They also have y-intercepts of y=0 and y=3, respectively.

Split the region up at y=1. Then the integral of f in the opposite order of variables is

\displaystyle \int_0^1 \int_0^{2y} f(x,y) \, dx \, dy + \int_1^3 \int_0^{3-y} f(x,y) \, dx \, dy

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