Sr Examen
Integral de cos^2(px\(3l))*A1^2*(p\(3l))^4 dx
Solución
Ha introducido
[src]
2*l / | | 4 | 2/p*x\ 2 / p \ | cos |---|*a1 *|---| dx | \3*l/ \3*l/ | / 0
$$\int\limits_{0}^{2 l} a_{1}^{2} \cos^{2}{\left(\frac{p x}{3 l} \right)} \left(\frac{p}{3 l}\right)^{4}\, dx$$
Integral((cos((p*x)/((3*l)))^2*a1^2)*(p/((3*l)))^4, (x, 0, 2*l))
Respuesta (Indefinida)
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/ / x for p = 0\
| | |
| | /2*p*x\ |
/ | <3*l*sin|-----| |
| | | \ 3*l / |
| 4 4 | |-------------- otherwise|
| 2/p*x\ 2 / p \ 2 p |x \ 2*p |
| cos |---|*a1 *|---| dx = C + a1 *-----*|- + --------------------------|
| \3*l/ \3*l/ 4 \2 2 /
| 81*l
/
$$\int a_{1}^{2} \cos^{2}{\left(\frac{p x}{3 l} \right)} \left(\frac{p}{3 l}\right)^{4}\, dx = C + a_{1}^{2} \frac{p^{4}}{81 l^{4}} \left(\frac{x}{2} + \frac{\begin{cases} x & \text{for}\: p = 0 \\\frac{3 l \sin{\left(\frac{2 p x}{3 l} \right)}}{2 p} & \text{otherwise} \end{cases}}{2}\right)$$
Respuesta
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/ / /2*p\ /2*p\\ | | cos|---|*sin|---|| | 2 3 |p \ 3 / \ 3 /| |a1 *p *|- + -----------------| | \3 2 / p |------------------------------ for --- != 0 | 3 3*l < 27*l | | 2 4 | 2*a1 *p | -------- otherwise | 3 | 81*l \
$$\begin{cases} \frac{a_{1}^{2} p^{3} \left(\frac{p}{3} + \frac{\sin{\left(\frac{2 p}{3} \right)} \cos{\left(\frac{2 p}{3} \right)}}{2}\right)}{27 l^{3}} & \text{for}\: \frac{p}{3 l} \neq 0 \\\frac{2 a_{1}^{2} p^{4}}{81 l^{3}} & \text{otherwise} \end{cases}$$
=
=
/ / /2*p\ /2*p\\ | | cos|---|*sin|---|| | 2 3 |p \ 3 / \ 3 /| |a1 *p *|- + -----------------| | \3 2 / p |------------------------------ for --- != 0 | 3 3*l < 27*l | | 2 4 | 2*a1 *p | -------- otherwise | 3 | 81*l \
$$\begin{cases} \frac{a_{1}^{2} p^{3} \left(\frac{p}{3} + \frac{\sin{\left(\frac{2 p}{3} \right)} \cos{\left(\frac{2 p}{3} \right)}}{2}\right)}{27 l^{3}} & \text{for}\: \frac{p}{3 l} \neq 0 \\\frac{2 a_{1}^{2} p^{4}}{81 l^{3}} & \text{otherwise} \end{cases}$$
Piecewise((a1^2*p^3*(p/3 + cos(2*p/3)*sin(2*p/3)/2)/(27*l^3), Ne(p/(3*l), 0)), (2*a1^2*p^4/(81*l^3), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.