Sr Examen
Integral de xcos(pi*sqrt(x)) dx
Solución
Ha introducido
[src]
1 / | | / ___\ | x*cos\pi*\/ x / dx | / -1
$$\int\limits_{-1}^{1} x \cos{\left(\pi \sqrt{x} \right)}\, dx$$
Integral(x*cos(pi*sqrt(x)), (x, -1, 1))
Respuesta (Indefinida)
[src]
/ | / ___\ ___ / ___\ 3/2 / ___\ / ___\ | / ___\ 12*cos\pi*\/ x / 12*\/ x *sin\pi*\/ x / 2*x *sin\pi*\/ x / 6*x*cos\pi*\/ x / | x*cos\pi*\/ x / dx = C - ---------------- - ---------------------- + -------------------- + ----------------- | 4 3 pi 2 / pi pi pi
$$\int x \cos{\left(\pi \sqrt{x} \right)}\, dx = C + \frac{2 x^{\frac{3}{2}} \sin{\left(\pi \sqrt{x} \right)}}{\pi} - \frac{12 \sqrt{x} \sin{\left(\pi \sqrt{x} \right)}}{\pi^{3}} + \frac{6 x \cos{\left(\pi \sqrt{x} \right)}}{\pi^{2}} - \frac{12 \cos{\left(\pi \sqrt{x} \right)}}{\pi^{4}}$$
Gráfica
Respuesta
[src]
6 12 12*sinh(pi) 2*sinh(pi) 6*cosh(pi) 12*cosh(pi)
- --- + --- - ----------- - ---------- + ---------- + -----------
2 4 3 pi 2 4
pi pi pi pi pi
$$- \frac{2 \sinh{\left(\pi \right)}}{\pi} - \frac{12 \sinh{\left(\pi \right)}}{\pi^{3}} - \frac{6}{\pi^{2}} + \frac{12}{\pi^{4}} + \frac{12 \cosh{\left(\pi \right)}}{\pi^{4}} + \frac{6 \cosh{\left(\pi \right)}}{\pi^{2}}$$
=
=
6 12 12*sinh(pi) 2*sinh(pi) 6*cosh(pi) 12*cosh(pi)
- --- + --- - ----------- - ---------- + ---------- + -----------
2 4 3 pi 2 4
pi pi pi pi pi
$$- \frac{2 \sinh{\left(\pi \right)}}{\pi} - \frac{12 \sinh{\left(\pi \right)}}{\pi^{3}} - \frac{6}{\pi^{2}} + \frac{12}{\pi^{4}} + \frac{12 \cosh{\left(\pi \right)}}{\pi^{4}} + \frac{6 \cosh{\left(\pi \right)}}{\pi^{2}}$$
-6/pi^2 + 12/pi^4 - 12*sinh(pi)/pi^3 - 2*sinh(pi)/pi + 6*cosh(pi)/pi^2 + 12*cosh(pi)/pi^4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.