Evaluate by contour integration ∫ 0 ∞ cos 2 ( α π / 2 ) 1 − α 2 2 d α . Hint: cos 2 ( α π / 2 ) = ( 1 + cos α π ) / 2. Evaluate ∮ 1 + e i π z ( z − 1 ) 2 ( z + 1 ) 2 d z around the upper half plane; note that the poles are actually simple poles (see Section 7 , Example 4 ) .
Evaluate by contour integration ∫ 0 ∞ cos 2 ( α π / 2 ) 1 − α 2 2 d α . Hint: cos 2 ( α π / 2 ) = ( 1 + cos α π ) / 2. Evaluate ∮ 1 + e i π z ( z − 1 ) 2 ( z + 1 ) 2 d z around the upper half plane; note that the poles are actually simple poles (see Section 7 , Example 4 ) .
Evaluate by contour integration
∫
0
∞
cos
2
(
α
π
/
2
)
1
−
α
2
2
d
α
.
Hint:
cos
2
(
α
π
/
2
)
=
(
1
+
cos
α
π
)
/
2.
Evaluate
∮
1
+
e
i
π
z
(
z
−
1
)
2
(
z
+
1
)
2
d
z
around the upper half plane; note that the poles are actually simple poles (see Section
7
,
Example
4
)
.
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.
Integrate S(cos x)e*+sin xdx
B. et-sinx +C
A. -e++sin x + C
c. e++sinx + c
D. e-4+sin x + C
A
В
C
D
Evaluate
Se²x
2x
Se²x
2x
cos (5x) dx.
cos (5x) dx =
e2x. (5 sin (5x) + 2 cos (5x))
19
+ C
If x*y" + xy +(x? -y3D
x>0 V1=x 2sinx
and y=y,v. Which of the following
equations satisfied by v
Select one:
a.
(x 2 sinx)v" + (2x2 cosx)v' =0
O b.
(x sinx)y" + (2x cosx-xsinx+xsinx)v =0
cosx - x 2 sinx+x2 sinx)v =0
C.
(x 2 sinx)v" + (2x 2 cosx)v =0
(x 2 sinx)v" + (2x 2 cosx)v=0
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY