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(Solved): Let f(x,y)=x^(2)e^(x^(2)) and let R be the triangle bounded by the lines x=5,x=(y)/(3), and y=x in t ...
Let
f(x,y)=x^(2)e^(x^(2))and let
Rbe the triangle bounded by the lines
x=5,x=(y)/(3), and
y=xin the
xy-plane. (a) Express
\int_R fdAas 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 fdA=\int_a^b \int_c^d f(x,y)dy
?
dx
?where
a=0,?,b=5,?,c=x,?, and
d=3x,?.
?
?And
\int_R fdA=\int_a^b \int_c^d f(x,y)dy
?(1)
dx
(C) \int_m^n \int_p^q f(x,y)dy(1)
dx( ) where
a=
?0 (1),
b=
?5 (C),
c=(y)/(3)
?
(y)/(3)(1)
_(_())_(_())
d=y
_(_())_(_())(1)
m=
?0 (1),
n=
?15 (?),
p=
?(1), and
q=
?5 (1). (b) Evaluate one of your integrals to find the value of
\int_R fdA.
\int_R fdA=?