Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be useful. 11. ∫ 0 π / 2 ∫ 0 1 ∫ 0 π / 2 sin π x cos y sin 2 z d y d x d z
Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be useful. 11. ∫ 0 π / 2 ∫ 0 1 ∫ 0 π / 2 sin π x cos y sin 2 z d y d x d z
Solution Summary: The author evaluates the value of the given triple integral, which is 2pi.
Integrals over boxesEvaluate the following integrals. A sketch of the region of integration may be useful.
11.
∫
0
π
/
2
∫
0
1
∫
0
π
/
2
sin
π
x
cos
y
sin
2
z
d
y
d
x
d
z
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.
Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below.
Let g(x) = √ƒƒ(t) dt .
0
3
2
-2
2
4
5
6
7
8
9
10
11
12
13
14
15
1. g(0) =
2. g(2) =
3. g(4) =
4. g(6) =
5. g'(3) =
6. g'(13)=
The expression 3 | (3+1/+1)
of the following integrals?
A
Ов
E
+
+
+ +
18
3+1+1
3++1
3++1
(A) √2×14 dx
x+1
(C) 1½-½√ √ ² ( 14 ) d x
(B) √31dx
(D) So 3+x
-dx
is a Riemann sum approximation of which
5
(E) 1½√√3dx
2x+1
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
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Numerical Integration Introduction l Trapezoidal Rule Simpson's 1/3 Rule l Simpson's 3/8 l GATE 2021; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=zadUB3NwFtQ;License: Standard YouTube License, CC-BY