Sr Examen
Integral de e^(-3x/2)*sin(pi*n*x) dx
Solución
Ha introducido
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1/2 / | | -3*x | ---- | 2 | E *sin(pi*n*x) dx | / -1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} e^{\frac{\left(-1\right) 3 x}{2}} \sin{\left(x \pi n \right)}\, dx$$
Integral(E^((-3*x)/2)*sin((pi*n)*x), (x, -1/2, 1/2))
Respuesta (Indefinida)
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/ / | | | -3*x | -3*x | ---- | ---- | 2 | 2 | E *sin(pi*n*x) dx = C + | e *sin(pi*n*x) dx | | / /
$$\int e^{\frac{\left(-1\right) 3 x}{2}} \sin{\left(x \pi n \right)}\, dx = C + \int e^{- \frac{3 x}{2}} \sin{\left(x \pi n \right)}\, dx$$
Respuesta
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/pi*n\ /pi*n\ /pi*n\ /pi*n\
6*sin|----| 6*sin|----| 4*pi*n*cos|----| 4*pi*n*cos|----|
\ 2 / \ 2 / \ 2 / \ 2 /
- ------------------------ - ---------------------- - ---------------------- + ------------------------
-3/4 2 2 -3/4 3/4 2 2 3/4 3/4 2 2 3/4 -3/4 2 2 -3/4
9*e + 4*pi *n *e 9*e + 4*pi *n *e 9*e + 4*pi *n *e 9*e + 4*pi *n *e
$$- \frac{4 \pi n \cos{\left(\frac{\pi n}{2} \right)}}{4 \pi^{2} n^{2} e^{\frac{3}{4}} + 9 e^{\frac{3}{4}}} + \frac{4 \pi n \cos{\left(\frac{\pi n}{2} \right)}}{\frac{4 \pi^{2} n^{2}}{e^{\frac{3}{4}}} + \frac{9}{e^{\frac{3}{4}}}} - \frac{6 \sin{\left(\frac{\pi n}{2} \right)}}{4 \pi^{2} n^{2} e^{\frac{3}{4}} + 9 e^{\frac{3}{4}}} - \frac{6 \sin{\left(\frac{\pi n}{2} \right)}}{\frac{4 \pi^{2} n^{2}}{e^{\frac{3}{4}}} + \frac{9}{e^{\frac{3}{4}}}}$$
=
=
/pi*n\ /pi*n\ /pi*n\ /pi*n\
6*sin|----| 6*sin|----| 4*pi*n*cos|----| 4*pi*n*cos|----|
\ 2 / \ 2 / \ 2 / \ 2 /
- ------------------------ - ---------------------- - ---------------------- + ------------------------
-3/4 2 2 -3/4 3/4 2 2 3/4 3/4 2 2 3/4 -3/4 2 2 -3/4
9*e + 4*pi *n *e 9*e + 4*pi *n *e 9*e + 4*pi *n *e 9*e + 4*pi *n *e
$$- \frac{4 \pi n \cos{\left(\frac{\pi n}{2} \right)}}{4 \pi^{2} n^{2} e^{\frac{3}{4}} + 9 e^{\frac{3}{4}}} + \frac{4 \pi n \cos{\left(\frac{\pi n}{2} \right)}}{\frac{4 \pi^{2} n^{2}}{e^{\frac{3}{4}}} + \frac{9}{e^{\frac{3}{4}}}} - \frac{6 \sin{\left(\frac{\pi n}{2} \right)}}{4 \pi^{2} n^{2} e^{\frac{3}{4}} + 9 e^{\frac{3}{4}}} - \frac{6 \sin{\left(\frac{\pi n}{2} \right)}}{\frac{4 \pi^{2} n^{2}}{e^{\frac{3}{4}}} + \frac{9}{e^{\frac{3}{4}}}}$$
-6*sin(pi*n/2)/(9*exp(-3/4) + 4*pi^2*n^2*exp(-3/4)) - 6*sin(pi*n/2)/(9*exp(3/4) + 4*pi^2*n^2*exp(3/4)) - 4*pi*n*cos(pi*n/2)/(9*exp(3/4) + 4*pi^2*n^2*exp(3/4)) + 4*pi*n*cos(pi*n/2)/(9*exp(-3/4) + 4*pi^2*n^2*exp(-3/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.