Sr Examen
Integral de cos(pi*t+32*pi)+2sin(√2∙(pi*t+32*pi)) dx
Solución
Ha introducido
[src]
1/8 / | | / / ___ \\ | \cos(pi*t + 32*pi) + 2*sin\\/ 2 *(pi*t + 32*pi)// dt | / 0
$$\int\limits_{0}^{\frac{1}{8}} \left(2 \sin{\left(\sqrt{2} \left(\pi t + 32 \pi\right) \right)} + \cos{\left(\pi t + 32 \pi \right)}\right)\, dt$$
Integral(cos(pi*t + 32*pi) + 2*sin(sqrt(2)*(pi*t + 32*pi)), (t, 0, 1/8))
Respuesta (Indefinida)
[src]
/ | ___ / ___ \ | / / ___ \\ sin(pi*t) \/ 2 *cos\\/ 2 *(pi*t + 32*pi)/ | \cos(pi*t + 32*pi) + 2*sin\\/ 2 *(pi*t + 32*pi)// dt = C + --------- - ------------------------------- | pi pi /
$$\int \left(2 \sin{\left(\sqrt{2} \left(\pi t + 32 \pi\right) \right)} + \cos{\left(\pi t + 32 \pi \right)}\right)\, dt = C + \frac{\sin{\left(\pi t \right)}}{\pi} - \frac{\sqrt{2} \cos{\left(\sqrt{2} \left(\pi t + 32 \pi\right) \right)}}{\pi}$$
Gráfica
Respuesta
[src]
___________
/ ___ / ___\
/ 1 \/ 2 ___ |257*pi*\/ 2 |
/ - - ----- ___ / ___\ \/ 2 *cos|------------|
\/ 2 4 \/ 2 *cos\32*pi*\/ 2 / \ 8 /
---------------- + ---------------------- - -----------------------
pi pi pi
$$\frac{\sqrt{2} \cos{\left(32 \sqrt{2} \pi \right)}}{\pi} - \frac{\sqrt{2} \cos{\left(\frac{257 \sqrt{2} \pi}{8} \right)}}{\pi} + \frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{\pi}$$
=
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___________
/ ___ / ___\
/ 1 \/ 2 ___ |257*pi*\/ 2 |
/ - - ----- ___ / ___\ \/ 2 *cos|------------|
\/ 2 4 \/ 2 *cos\32*pi*\/ 2 / \ 8 /
---------------- + ---------------------- - -----------------------
pi pi pi
$$\frac{\sqrt{2} \cos{\left(32 \sqrt{2} \pi \right)}}{\pi} - \frac{\sqrt{2} \cos{\left(\frac{257 \sqrt{2} \pi}{8} \right)}}{\pi} + \frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{\pi}$$
sqrt(1/2 - sqrt(2)/4)/pi + sqrt(2)*cos(32*pi*sqrt(2))/pi - sqrt(2)*cos(257*pi*sqrt(2)/8)/pi
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.