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 } 193. ∭ E ( sin x + sin y ) d V , where E = { ( x , y , z ) | 0 ≤ 1 x ≤ π 2 , − cos x ≤ 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 } 193. ∭ E ( sin x + sin y ) d V , where E = { ( x , y , z ) | 0 ≤ 1 x ≤ π 2 , − cos x ≤ 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
}
193.
∭
E
(
sin
x
+
sin
y
)
d
V
,
where
E
=
{
(
x
,
y
,
z
)
|
0
≤
1
x
≤
π
2
,
−
cos
x
≤
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.
I need help with B), both I and II, please. Thank you.
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.
pYdiscuss the integrabilty of the function f(x) = on [0,7).
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