Question

State Fubini's theorem.

Short answer

Ans: Then Fubini's theorem states as${\iint }_{R}f(x,y)dA={\int }_c^d{\int }_a^{b}f(x,y)dxdy={\int }_a^b{\int }_c^{d}f(x,y)dydx$

Step-by-step solution

Step 1. Given information: 

Fubini's theorem.

Step 2. Stating Fubini's theorem:

Fubini's theorem states that a double integral can be computed using iterated integrals, which means the order of integration can be switched for which the order chosen is easier to evaluate. Let $a<b$and $c<d$be real numbers, let R be the rectangle defined by $R=\left\{\right(x,y)\mid a\le x\le b$and $c\le y\le d\}$and let $f(x,y)$be continuous on R. Then Fubini's theorem states as

${\iint }_{R}f(x,y)dA={\int }_c^d{\int }_a^{b}f(x,y)dxdy={\int }_a^b{\int }_c^{d}f(x,y)dydx$