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
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
1. Let R denote the region below the graph of f(x) = /1 – x²
and above the interval [–1, 1].
(a) Use a geometric argument to find the area of R.
(b) What estimate results if the area of R is approximated by
the total area within the rectangles of the accompanying
figure?
A y
-1
_1
1
1
| Figure Ex-1
Chapter 7 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
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