In the following exercises, evaluate the triple integrals over the bounded legion E = { ( x , y , z ) | a ≤ x ≤ b , h 1 ( x ) ≤ y ≤ h 2 ( x ) , e ≤ z ≤ f } 192. ∭ E ( sin x + sin y ) d V , Where E = { ( x , y , z ) | 1 ≤ x ≤ e , 0 ≤ y ≤ cos x , − 1 ≤ z ≤ 1 }
In the following exercises, evaluate the triple integrals over the bounded legion E = { ( x , y , z ) | a ≤ x ≤ b , h 1 ( x ) ≤ y ≤ h 2 ( x ) , e ≤ z ≤ f } 192. ∭ E ( sin x + sin y ) d V , Where E = { ( x , y , z ) | 1 ≤ x ≤ e , 0 ≤ y ≤ cos x , − 1 ≤ z ≤ 1 }
In the following exercises, evaluate the triple integrals over the bounded legion
E
=
{
(
x
,
y
,
z
)
|
a
≤
x
≤
b
,
h
1
(
x
)
≤
y
≤
h
2
(
x
)
,
e
≤
z
≤
f
}
192.
∭
E
(
sin
x
+
sin
y
)
d
V
, Where
E
=
{
(
x
,
y
,
z
)
|
1
≤
x
≤
e
,
0
≤
y
≤
cos
x
,
−
1
≤
z
≤
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.
2. (Linearity of the integral)
Let I= [a₁, b₁] x ... x [an, bn] be a generalized rectangle in R". Suppose that the function
f: I→ R and g: I→ R are integrable, and a, 3 are real numbers. Prove that the function
af + Bg: IR is integrable and
Las
(af * + 8g) = a[ƒ + B [ g.
Show your argument step by step.
I need help with B), both I and II, please. Thank you.
Indicate whether the following statement is true or false.
Let f (x. y) be any c' real valued function defined on the rectangle R = [a, b] × [c, d].
Then S f(x, y) dy dx = [" Sª f (x, y) dx dy.
True
False
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