Matched Problem 4 Evaluate ∬ R ( y − 4 x ) d A , where R is the region in Example 4. Example 4 Evaluating a Double Integral Evaluate ∬ R ( 2 x + y ) d A , where R is the region bounded by the graphs of y = x , x + y = 2, and y = 0.
Matched Problem 4 Evaluate ∬ R ( y − 4 x ) d A , where R is the region in Example 4. Example 4 Evaluating a Double Integral Evaluate ∬ R ( 2 x + y ) d A , where R is the region bounded by the graphs of y = x , x + y = 2, and y = 0.
Solution Summary: The author evaluates the value of the iterated integral -7720.
Matched Problem 4 Evaluate
∬
R
(
y
−
4
x
)
d
A
, where R is the region in Example 4.
Example 4 Evaluating a Double Integral Evaluate
∬
R
(
2
x
+
y
)
d
A
, where R is the region bounded by the graphs of
y
=
x
, x + y = 2, and y = 0.
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
1. Let y = x² + 1 and y = −2x + 1.
(a) Graph the two functions together on the same plane. Find the points of intersection.
(b) Find the area of the region bounded by the line z = −2 on the left, the line x = 2
on the right, and the graphs of the functions y = x² + 1 and y = −2x + 1.
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
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