Q 8. - Calculus

Question

Which of the iterated integrals in Exercises below could correctly

be used to evaluate the double integral:

${\int }_2^6{\int }_1^{4}f(x,y)dxdy$

Step-by-Step Solution

Answer

The iterated integral will give correct value of ${\iint }_{R}f(x,y)dA$.

Step 1: Given Information

Rectangular region is bounded by lines $x=1,x=4,y=2\text{ and }y=6$.

Step 2: Simplification

Consider integral ${\int }_2^6{\int }_1^{4}f(x,y)dxdy$

For type II region, integration is done wrt $x$ first and then wrt $y$, Inner integral is solved wrt $x$.

In ${\int }_2^6{\int }_1^{4}f(x,y)dxdy$ also, inner integral is wrt $x$.

Hence, iterated integral will give correct value of ${\iint }_{R}f(x,y)dA$