Use both orders of iteration to evaluate each double integral Problems 27–30. 30. ∬ R x e y d A ; R = { ( x , y ) | − 2 ≤ x ≤ 3 , 0 ≤ y ≤ 2 }
Use both orders of iteration to evaluate each double integral Problems 27–30. 30. ∬ R x e y d A ; R = { ( x , y ) | − 2 ≤ x ≤ 3 , 0 ≤ y ≤ 2 }
Solution Summary: The author evaluates the area of the given integral over a given region. The upper and lower limits to x and y are shown in Figure 1.
Use both orders of iteration to evaluate each double integral Problems 27–30.
30.
∬
R
x
e
y
d
A
;
R
=
{
(
x
,
y
)
|
−
2
≤
x
≤
3
,
0
≤
y
≤
2
}
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.
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
=
Q6 What will be the allowable bearing capacity of sand having p = 37° and ydry
19 kN/m³ for (i) 1.5 m strip foundation (ii) 1.5 m x 1.5 m square footing and
(iii)1.5m x 2m rectangular footing. The footings are placed at a depth of 1.5 m
below ground level. Assume F, = 2.5. Use Terzaghi's equations.
0
Ne
Na
Ny
35 57.8 41.4 42.4
40 95.7 81.3 100.4
Q1 The SPT records versus depth are given in table below. Find qan for the raft 12%
foundation with BxB-10x10m and depth of raft D-2m, the allowable
settlement is 50mm.
Elevation, m 0.5 2
2 6.5 9.5 13 18 25
No.of blows, N 11 15 29 32 30 44
0
estigate shear
12%
Chapter 7 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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