Matched Problem 3 Evaluate ∬ R 3 x y 2 d A , where R is the region in Example 3. Example 3 Evaluating a Double Integral Evaluate ∬ R 2 x y d A , where R is the region bounded by the graphs of y = − x and y = x 2 , x ≥ 0, and the graph of x = 1.
Matched Problem 3 Evaluate ∬ R 3 x y 2 d A , where R is the region in Example 3. Example 3 Evaluating a Double Integral Evaluate ∬ R 2 x y d A , where R is the region bounded by the graphs of y = − x and y = x 2 , x ≥ 0, and the graph of x = 1.
Solution Summary: The author evaluates the value of the iterated integral 1340.
Matched Problem 3 Evaluate
∬
R
3
x
y
2
d
A
, where R is the region in Example 3.
Example 3 Evaluating a Double Integral Evaluate
∬
R
2
x
y
d
A
, where R is the region bounded by the graphs of y = −x and y = x2, x ≥ 0, and the graph of x = 1.
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.
3. The region between the graphs of y = x3 + 4x - 1 and y = 2x3+ 3x2 - 1
2)Let f(x) =2x-6
Let x0 be the x coordinate of x intercept of f(x) and y0 be the y coordinate of f(x) then
x0=
y0=
The area of the region bounded by f(x),x axis over interval [0,x0] is
Consider the following.
x3
X
6 - X
y =
y = 0
x = 5
(a) Use a graphing utility to graph the region bounded by the graphs of the equations.
12
10
8
y 6-
2
12
10
8
y 6-
2
T
2
3
X
4
5
y 3
2-
0
12
10
8
y 6-
2-
0.5
1
1.5 2
X
2.5
3
3.5
Chapter 7 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
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