Let $f(x,y)=x^2e^{x^2}$ and let $R$ be the triangle bounded by the lines $x=2$, $x=y/3$, and $y=x$ in the $xy$-plane.

(a) Express $\int_R{f}\,dA$ as a double integral in two different ways by filling in the values for the integrals below. (For one of these it will be necessary to write the double integral as a sum of two integrals, as indicated; for the other, it can be written as a single integral.)

$\int_R{f}\,dA = \int_a^b\int_c^d f(x,y)\, d$ $d$
where $a =$ , $b =$ , $c =$ , and $d =$ .

And $\int_R{f}\,dA = \int_a^b\int_c^d f(x,y)\, d$ $d$ $+ \int_m^n\int_p^q f(x,y)\, d$ $d$
where $a =$ , $b =$ , $c =$ , $d =$ , $m =$ , $n =$ , $p =$ , and $q =$ .

(b) Evaluate one of your integrals to find the value of $\int_R{f}\,dA$.
$\int_R{f}\,dA =$