Solutions > Sequences First Term Calculator >

Sequences First Term Calculator

Topic

Full pad

`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for expand factor rationalize

See All

area

asymptotes

critical points

derivative

domain

eigenvalues

eigenvectors

expand

extreme points

factor

implicit derivative

inflection points

intercepts

inverse

laplace

inverse laplace

partial fractions

range

slope

simplify

solve for

tangent

taylor

vertex

geometric test

alternating test

telescoping test

pseries test

root test

Steps Examples

Generated by AI

série de fourier 12 x², [−L, L]

Solution

L²6 +∑_n=1^∞2(−1)ⁿL²cos(πnxL )π²n²

Show Steps

Hide Steps

Solution steps

One step at a time

12 x², [−L, L]

Série de Fourier

Série de Fourier de função f(x) no intervalo −L≤ x≤ L é definido como:
     f(x)=A₀+∑_n=1^∞A_n· cos(nπxL )+∑_n=1^∞B_n· sin(nπxL )
Onde
     A₀=12L · ∫_−L^Lf(x)dx
     A_n=1L · ∫_−L^Lf(x)cos(nπxL )dx,      n>0
     B_n=1L · ∫_−L^Lf(x)sin(nπxL )dx,      n>0

Aplique a fórmula de Fourier

=12L · ∫_−L^L12 x²dx+∑_n=1^∞1L · ∫_−L^L12 x²cos(nπxL )dx· cos(nπxL )+∑_n=1^∞1L · ∫_−L^L12 x²sin(nπxL )dx· sin(nπxL )

Resolva as integrais