X2 T05 02 trig by euler (2010)
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Transcript of X2 T05 02 trig by euler (2010)
![Page 1: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/1.jpg)
Trig Integrals with Euler
![Page 2: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/2.jpg)
Trig Integrals with Euler
xdx3sin
![Page 3: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/3.jpg)
Trig Integrals with Euler
xdx3sin 3 31 3 38
ix ix ix ixe e e e dxi
![Page 4: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/4.jpg)
Trig Integrals with Euler
xdx3sin 3 31 3 38
ix ix ix ixe e e e dxi
3 31 1 38 3
ix ix ix ixe e e e ci i i
![Page 5: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/5.jpg)
Trig Integrals with Euler
xdx3sin 3 31 3 38
ix ix ix ixe e e e dxi
3 31 1 38 3
ix ix ix ixe e e e ci i i
1 3cos3 cos
12 4x x c
![Page 6: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/6.jpg)
Trig Integrals with Euler
xdx3sin 3 31 3 38
ix ix ix ixe e e e dxi
3 31 1 38 3
ix ix ix ixe e e e ci i i
1 3cos3 cos
12 4x x c
31 34cos 3cos cos12 4
x x x c
![Page 7: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/7.jpg)
Trig Integrals with Euler
xdx3sin 3 31 3 38
ix ix ix ixe e e e dxi
3 31 1 38 3
ix ix ix ixe e e e ci i i
1 3cos3 cos
12 4x x c
31 34cos 3cos cos12 4
x x x c
31 1 3cos cos cos3 4 4
x x x c
![Page 8: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/8.jpg)
Trig Integrals with Euler
xdx3sin 3 31 3 38
ix ix ix ixe e e e dxi
3 31 1 38 3
ix ix ix ixe e e e ci i i
1 3cos3 cos
12 4x x c
31 34cos 3cos cos12 4
x x x c
31 1 3cos cos cos3 4 4
x x x c
31 cos cos3
x x c
![Page 9: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/9.jpg)
xdx4sin
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xdx4sin 4 2 2 41 4 6 416
ix ix ix ixe e e e dx
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xdx4sin 4 2 2 41 4 6 416
ix ix ix ixe e e e dx
4 4 2 21 1 2 616 4
ix ix ix ixe e e e x ci i
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xdx4sin 4 2 2 41 4 6 416
ix ix ix ixe e e e dx
4 4 2 21 1 2 616 4
ix ix ix ixe e e e x ci i
1 1 3sin 4 sin 232 4 8
x x x c
![Page 13: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/13.jpg)
xdx4sin 4 2 2 41 4 6 416
ix ix ix ixe e e e dx
4 4 2 21 1 2 616 4
ix ix ix ixe e e e x ci i
1 1 3sin 4 sin 232 4 8
x x x c
xdx5sin
![Page 14: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/14.jpg)
xdx4sin 4 2 2 41 4 6 416
ix ix ix ixe e e e dx
4 4 2 21 1 2 616 4
ix ix ix ixe e e e x ci i
1 1 3sin 4 sin 232 4 8
x x x c
xdx5sin 5 3 3 51 5 10 10 532
ix ix ix ix ix ixe e e e e e dxi
![Page 15: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/15.jpg)
xdx4sin 4 2 2 41 4 6 416
ix ix ix ixe e e e dx
4 4 2 21 1 2 616 4
ix ix ix ixe e e e x ci i
1 1 3sin 4 sin 232 4 8
x x x c
xdx5sin 5 3 3 51 5 10 10 532
ix ix ix ix ix ixe e e e e e dxi
5 5 3 31 1 5 1032 5 3
ix ix ix ix ix ixe e e e e e ci i i i
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xdx4sin 4 2 2 41 4 6 416
ix ix ix ixe e e e dx
4 4 2 21 1 2 616 4
ix ix ix ixe e e e x ci i
1 1 3sin 4 sin 232 4 8
x x x c
xdx5sin 5 3 3 51 5 10 10 532
ix ix ix ix ix ixe e e e e e dxi
5 5 3 31 1 5 1032 5 3
ix ix ix ix ix ixe e e e e e ci i i i
1 5 5sin5 cos3 cos
80 48 8x x x c
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5 3cos sinx xdx
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5 3cos sinx xdx 5 31256
ix ix ix ixe e e e dxi
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5 3cos sinx xdx 5 31256
ix ix ix ixe e e e dxi
2 32 21
256ix ix ix ixe e e e dx
i
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5 3cos sinx xdx 5 31256
ix ix ix ixe e e e dxi
2 32 21
256ix ix ix ixe e e e dx
i
2 2 6 2 2 61 2 3 3256
ix ix ix ix ix ixe e e e e e dxi
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5 3cos sinx xdx 5 31256
ix ix ix ixe e e e dxi
2 32 21
256ix ix ix ixe e e e dx
i
2 2 6 2 2 61 2 3 3256
ix ix ix ix ix ixe e e e e e dxi
8 4 4 6 2 2 6
4 4 8
1 ( 3 3 2 6 6 2256
3 3 )
ix ix ix ix ix ix ix
ix ix ix
e e e e e e ei
e e e dx
![Page 22: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/22.jpg)
5 3cos sinx xdx 5 31256
ix ix ix ixe e e e dxi
2 32 21
256ix ix ix ixe e e e dx
i
2 2 6 2 2 61 2 3 3256
ix ix ix ix ix ixe e e e e e dxi
8 4 4 6 2 2 6
4 4 8
1 ( 3 3 2 6 6 2256
3 3 )
ix ix ix ix ix ix ix
ix ix ix
e e e e e e ei
e e e dx
8 8 6 6 4 4 2 21 1 1 1 3256 8 3 2
ix ix ix ix ix ix ix ixe e e e e e e ei i i i i
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5 3cos sinx xdx 5 31256
ix ix ix ixe e e e dxi
2 32 21
256ix ix ix ixe e e e dx
i
2 2 6 2 2 61 2 3 3256
ix ix ix ix ix ixe e e e e e dxi
8 4 4 6 2 2 6
4 4 8
1 ( 3 3 2 6 6 2256
3 3 )
ix ix ix ix ix ix ix
ix ix ix
e e e e e e ei
e e e dx
8 8 6 6 4 4 2 21 1 1 1 3256 8 3 2
ix ix ix ix ix ix ix ixe e e e e e e ei i i i i
1 1 1 3cos8 cos6 cos 4 cos 21024 384 256 128
x x x x c
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6 3sin cosx xdx
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6 3sin cosx xdx 3 61512
ix ix ix ixe e e e dx
![Page 26: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/26.jpg)
6 3sin cosx xdx 3 61512
ix ix ix ixe e e e dx
3 32 21512
ix ix ix ixe e e e dx
![Page 27: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/27.jpg)
6 3sin cosx xdx 3 61512
ix ix ix ixe e e e dx
3 32 21512
ix ix ix ixe e e e dx 3 3 6 2 2 61 3 3 3 3
512ix ix ix ix ix ix ix ixe e e e e e e e dx
![Page 28: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/28.jpg)
6 3sin cosx xdx 3 61512
ix ix ix ixe e e e dx
3 32 21512
ix ix ix ixe e e e dx 3 3 6 2 2 61 3 3 3 3
512ix ix ix ix ix ix ix ixe e e e e e e e dx
9 9 7 7 3 31 3 8 6512
ix ix ix ix ix ix ix ixe e e e e e e e dx
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6 3sin cosx xdx 3 61512
ix ix ix ixe e e e dx
3 32 21512
ix ix ix ixe e e e dx 3 3 6 2 2 61 3 3 3 3
512ix ix ix ix ix ix ix ixe e e e e e e e dx
9 9 7 7 3 31 3 8 6512
ix ix ix ix ix ix ix ixe e e e e e e e dx
9 9 7 7 3 31 1 3 8 6512 9 7 3
ix ix ix ix ix ix ix ixe e e e e e e e ci i i i
![Page 30: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/30.jpg)
6 3sin cosx xdx 3 61512
ix ix ix ixe e e e dx
3 32 21512
ix ix ix ixe e e e dx 3 3 6 2 2 61 3 3 3 3
512ix ix ix ix ix ix ix ixe e e e e e e e dx
9 9 7 7 3 31 3 8 6512
ix ix ix ix ix ix ix ixe e e e e e e e dx
9 9 7 7 3 31 1 3 8 6512 9 7 3
ix ix ix ix ix ix ix ixe e e e e e e e ci i i i
1 3 1 3sin 9 sin 7 sin 3 sin2304 1792 96 128
x x x x c
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2 2sin cosx xdx
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2 2sin cosx xdx 2 2116
ix ix ix ixe e e e dx
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2 2sin cosx xdx 2 2116
ix ix ix ixe e e e dx
22 2116
ix ixe e dx
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2 2sin cosx xdx 2 2116
ix ix ix ixe e e e dx
22 2116
ix ixe e dx
4 41 216
ix ixe e dx
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2 2sin cosx xdx 2 2116
ix ix ix ixe e e e dx
22 2116
ix ixe e dx
4 41 216
ix ixe e dx
4 41 1 216 4
ix ixe e x ci
![Page 36: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/36.jpg)
2 2sin cosx xdx 2 2116
ix ix ix ixe e e e dx
22 2116
ix ixe e dx
4 41 216
ix ixe e dx
4 41 1 216 4
ix ixe e x ci
1 1sin 432 8
x x c
![Page 37: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/37.jpg)
sintancos
xxx
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sintancos
xxx
ix ix
ix ix
e ei e e
![Page 39: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/39.jpg)
sintancos
xxx
ix ix
ix ix
e ei e e
xdx3tan
![Page 40: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/40.jpg)
sintancos
xxx
ix ix
ix ix
e ei e e
xdx3tan3
1 ix ix
ix ix
e e dxi e e
![Page 41: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/41.jpg)
sintancos
xxx
ix ix
ix ix
e ei e e
xdx3tan3
1 ix ix
ix ix
e e dxi e e
TOO MUCH WORK INVOLVED COMPARED TO PREVIOUS METHOD
![Page 42: X2 T05 02 trig by euler (2010)](https://reader033.fdocument.pub/reader033/viewer/2022052606/58edbf801a28ab9f218b45f3/html5/thumbnails/42.jpg)
sintancos
xxx
ix ix
ix ix
e ei e e
xdx3tan3
1 ix ix
ix ix
e e dxi e e
TOO MUCH WORK INVOLVED COMPARED TO PREVIOUS METHOD
IF USING EULER’S, STICK WITH FUNCTIONS INVOLVING SINX OR COSX