Question

Let f(x,y)=x2ex2f(x,y)=x2ex2 and let RR be the triangle bounded by the lines x=2x=2, x=y/3x=y/3, and y=xy=x in the xyxy-plane.

(a) Express ∫RfdA∫RfdA 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.)

∫RfdA=∫ba∫dcf(x,y)d∫RfdA=∫ab∫cdf(x,y)d dd
where a=a=  , b=b=  , c=c=  , and d=d=  .

And ∫RfdA=∫ba∫dcf(x,y)d∫RfdA=∫ab∫cdf(x,y)d dd +∫nm∫qpf(x,y)d+∫mn∫pqf(x,y)d dd
where

Answer 1