Sr Examen
Integral de ((sin(pi*x/2))^6)*((cos(pi*x/2))^14) dx
Solución
Ha introducido
[src]
1 / | | 6/pi*x\ 14/pi*x\ | sin |----|*cos |----| dx | \ 2 / \ 2 / | / 0
$$\int\limits_{0}^{1} \sin^{6}{\left(\frac{\pi x}{2} \right)} \cos^{14}{\left(\frac{\pi x}{2} \right)}\, dx$$
Integral(sin((pi*x)/2)^6*cos((pi*x)/2)^14, (x, 0, 1))
Respuesta (Indefinida)
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/ 15/pi*x\ /pi*x\ 19/pi*x\ /pi*x\ 13/pi*x\ /pi*x\ 11/pi*x\ /pi*x\ 17/pi*x\ /pi*x\ /pi*x\ /pi*x\ 3/pi*x\ /pi*x\ 5/pi*x\ /pi*x\ 7/pi*x\ /pi*x\ 9/pi*x\ /pi*x\\
| 383*cos |----|*sin|----| cos |----|*sin|----| cos |----|*sin|----| 13*cos |----|*sin|----| 41*cos |----|*sin|----| 143*cos|----|*sin|----| 143*cos |----|*sin|----| 143*cos |----|*sin|----| 143*cos |----|*sin|----| 143*cos |----|*sin|----||
/ | \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / 143*pi*x \ 2 / \ 2 / \ 2 / \ 2 /|
| 2*|- ------------------------- - --------------------- + --------------------- + ------------------------ + ------------------------ + ----------------------- + ------------------------ + ------------------------ + -------- + ------------------------ + ------------------------|
| 6/pi*x\ 14/pi*x\ \ 5760 20 5376 64512 360 262144 393216 491520 524288 573440 645120 /
| sin |----|*cos |----| dx = C + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| \ 2 / \ 2 / pi
|
/
$$\int \sin^{6}{\left(\frac{\pi x}{2} \right)} \cos^{14}{\left(\frac{\pi x}{2} \right)}\, dx = C + \frac{2 \left(\frac{143 \pi x}{524288} - \frac{\sin{\left(\frac{\pi x}{2} \right)} \cos^{19}{\left(\frac{\pi x}{2} \right)}}{20} + \frac{41 \sin{\left(\frac{\pi x}{2} \right)} \cos^{17}{\left(\frac{\pi x}{2} \right)}}{360} - \frac{383 \sin{\left(\frac{\pi x}{2} \right)} \cos^{15}{\left(\frac{\pi x}{2} \right)}}{5760} + \frac{\sin{\left(\frac{\pi x}{2} \right)} \cos^{13}{\left(\frac{\pi x}{2} \right)}}{5376} + \frac{13 \sin{\left(\frac{\pi x}{2} \right)} \cos^{11}{\left(\frac{\pi x}{2} \right)}}{64512} + \frac{143 \sin{\left(\frac{\pi x}{2} \right)} \cos^{9}{\left(\frac{\pi x}{2} \right)}}{645120} + \frac{143 \sin{\left(\frac{\pi x}{2} \right)} \cos^{7}{\left(\frac{\pi x}{2} \right)}}{573440} + \frac{143 \sin{\left(\frac{\pi x}{2} \right)} \cos^{5}{\left(\frac{\pi x}{2} \right)}}{491520} + \frac{143 \sin{\left(\frac{\pi x}{2} \right)} \cos^{3}{\left(\frac{\pi x}{2} \right)}}{393216} + \frac{143 \sin{\left(\frac{\pi x}{2} \right)} \cos{\left(\frac{\pi x}{2} \right)}}{262144}\right)}{\pi}$$
Gráfica
Respuesta
[src]
143 ------ 262144
$$\frac{143}{262144}$$
=
=
143 ------ 262144
$$\frac{143}{262144}$$
143/262144
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.