(a) Let f x , y = x 2 + y , and as shown in the accompanying figure, let the rectangle R = 0 , 2 × 0 , 2 be subdivided into 16 subrectangles. Take x k * , y k * to be the center of the k th rectangle, and approximate the double integral of f over R by the resulting Riemann sum. (b) Compare the result in part (a) to the exact value of the integral.
(a) Let f x , y = x 2 + y , and as shown in the accompanying figure, let the rectangle R = 0 , 2 × 0 , 2 be subdivided into 16 subrectangles. Take x k * , y k * to be the center of the k th rectangle, and approximate the double integral of f over R by the resulting Riemann sum. (b) Compare the result in part (a) to the exact value of the integral.
(a) Let
f
x
,
y
=
x
2
+
y
,
and as shown in the accompanying figure, let the rectangle
R
=
0
,
2
×
0
,
2
be subdivided into 16 subrectangles. Take
x
k
*
,
y
k
*
to be the center of the
k
th
rectangle, and approximate the double integral of
f
over
R
by the resulting Riemann sum.
(b) Compare the result in part (a) to the exact value of the integral.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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