Improper integrals Improper integrals arise in polar coordinates when the radial coordinate r becomes arbitrarily large. Under certain conditions, these integrals are treated in the usual way: ∫ α β ∫ a ∞ f ( r , θ ) r d r d θ = lim b → ∞ ∫ α β ∫ a b f ( r , θ ) r d r d θ . Use this technique to evaluate the following integrals. 64. ∬ R d A ( x 2 + y 2 ) 5 / 2 ; R = { ( r , θ ) : 1 ≤ r < ∞ , 0 ≤ θ ≤ 2 π }
Improper integrals Improper integrals arise in polar coordinates when the radial coordinate r becomes arbitrarily large. Under certain conditions, these integrals are treated in the usual way: ∫ α β ∫ a ∞ f ( r , θ ) r d r d θ = lim b → ∞ ∫ α β ∫ a b f ( r , θ ) r d r d θ . Use this technique to evaluate the following integrals. 64. ∬ R d A ( x 2 + y 2 ) 5 / 2 ; R = { ( r , θ ) : 1 ≤ r < ∞ , 0 ≤ θ ≤ 2 π }
Solution Summary: The author evaluates the value of the given integral, which is 2pi3.
Improper integralsImproper integrals arise in polar coordinates when the radial coordinate r becomes arbitrarily large. Under certain conditions, these integrals are treated in the usual way:
∫
α
β
∫
a
∞
f
(
r
,
θ
)
r
d
r
d
θ
=
lim
b
→
∞
∫
α
β
∫
a
b
f
(
r
,
θ
)
r
d
r
d
θ
.
Use this technique to evaluate the following integrals.
64.
∬
R
d
A
(
x
2
+
y
2
)
5
/
2
;
R
=
{
(
r
,
θ
)
:
1
≤
r
<
∞
,
0
≤
θ
≤
2
π
}
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.
(1 point) Evaluate the iterated integral by converting to polar coordinates.
NOTE: When typing your answers use "th" for 0.
/6-y2
2x + 4y dx dy
Σ
dr de
=
where
a =
Σ
b =
pi/2
Σ
c =
Σ
d =
6-y2
2x + 4y dx dy =
Σ
M M MM
(3) Evaluate the iterated integral by converting to polar coordinates.
4-y2
(x + y) dx dy
0,
Green’s Theorem for line integrals Use either form of Green’sTheorem to evaluate the following line integral.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY