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Integrales de coeficiente, Study Guides, Projects, Research of Mathematics

Antillean Adventist University (AAU)Mathematics

Integrales comunes para universidad, espero les ayude aunque solo quiero ver un documento pero fue un dorm

Typology: Study Guides, Projects, Research

2022/2023

Uploaded on 02/09/2025

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Integrales frecuentes resueltas
que se usan en el cĀ“alculo de los
Coeficientes de Fourier
En principio hay que tener en cuenta las siguientes expresiones:
cos (nĻ€) = (āˆ’1)ndonde nāˆˆN(1)
sin (nĻ€) = 0 donde nāˆˆN(2)
A continuaciĀ“on mostramos la soluciĀ“on de las integrales que con mĀ“as frecuen-
cia suelen aparecer en el cĀ“alculo de los Coeficientes de Fourier. Al usarlas
podremos ahorrar tiempo y sobre todo muchos posibles errores.
a, b, c āˆˆR
Zxcos (ax)dx =1
a2cos (ax) + x
asin (ax) + c (3)
Zxsin (ax)dx =1
a2sin (ax)āˆ’x
acos (ax) + c (4)
Zx2cos (ax)dx =2x
a2cos (ax) + ī˜’x2
aāˆ’2
a3ī˜“sin (ax) + c (5)
Zx2sin (ax)dx =2x
a2sin (ax)āˆ’ī˜’x2
aāˆ’2
a3ī˜“cos (ax) + c (6)
Zx3cos (ax)dx =ī˜’3x2
a2āˆ’6
a4ī˜“cos (ax) + ī˜’x3
aāˆ’6x
a3ī˜“sin (ax) + c (7)
Zx3sin (ax)dx =ī˜’3x2
a2āˆ’6
a4ī˜“sin (ax)āˆ’ī˜’x3
aāˆ’6x
a3ī˜“cos (ax) + c (8)
Zeax cos (bx)dx =eax
a2+b2(arccos (bx) + bsin (bx)) + c (9)
Zeax sin (bx)dx =eax
a2+b2(arcsin (bx)āˆ’bcos (bx)) + c (10)
Este formulario ha sido creado por @famarnez, el profesor del canal de
YouTube fĀ“ısicaymates. Se permite su libre distribuciĀ“on y/o modificaciĀ“on
siempre que se mantenga la referencia a su autor y a dicho canal de YouTube.
Visita https://fisicaymates.com donde encontrarĀ“as mĀ“as material de es-
tudio.
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Integrales frecuentes resueltas

que se usan en el cĀ“alculo de los

Coeficientes de Fourier

En principio hay que tener en cuenta las siguientes expresiones:

cos (nĻ€) = (āˆ’1)n^ donde n āˆˆ N (1) sin (nĻ€) = 0 donde n āˆˆ N (2)

A continuaciĀ“on mostramos la soluciĀ“on de las integrales que con mĀ“as frecuen- cia suelen aparecer en el cĀ“alculo de los Coeficientes de Fourier. Al usarlas podremos ahorrar tiempo y sobre todo muchos posibles errores.

a, b, c āˆˆ R

āˆ« x cos (ax) dx =

a^2 cos (ax) + x a sin (ax) + c (3) āˆ« x sin (ax) dx =

a^2 sin (ax) āˆ’ x a cos (ax) + c (4) āˆ« x^2 cos (ax) dx = 2 x a^2 cos (ax) +

x^2 a

a^3

sin (ax) + c (5) āˆ« x^2 sin (ax) dx = 2 x a^2 sin (ax) āˆ’

x^2 a

a^3

cos (ax) + c (6) āˆ« x^3 cos (ax) dx =

3 x^2 a^2

a^4

cos (ax) +

x^3 a

6 x a^3

sin (ax) + c (7) āˆ« x^3 sin (ax) dx =

3 x^2 a^2

a^4

sin (ax) āˆ’

x^3 a

6 x a^3

cos (ax) + c (8) āˆ« eax^ cos (bx) dx = eax a^2 + b^2 (arccos (bx) + b sin (bx)) + c (9) āˆ« eax^ sin (bx) dx = eax a^2 + b^2 (arcsin (bx) āˆ’ b cos (bx)) + c (10)

Este formulario ha sido creado por @famarnez, el profesor del canal de YouTube fĀ“ısicaymates. Se permite su libre distribuciĀ“on y/o modificaciĀ“on siempre que se mantenga la referencia a su autor y a dicho canal de YouTube. Visita https://fisicaymates.com donde encontrarĀ“as mĀ“as material de es- tudio.

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