Sr Examen
Integral de (sin^6)*x*cosxdx dx
Solución
Ha introducido
[src]
1 / | | 6 | sin (x)*x*cos(x) dx | / 0
$$\int\limits_{0}^{1} x \sin^{6}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral((sin(x)^6*x)*cos(x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 7 7 6 3 4 5 2 | 6 16*cos (x) x*sin (x) sin (x)*cos(x) 2*cos (x)*sin (x) 8*cos (x)*sin (x) | sin (x)*x*cos(x) dx = C + ---------- + --------- + -------------- + ----------------- + ----------------- | 245 7 7 7 35 /
$$\int x \sin^{6}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{x \sin^{7}{\left(x \right)}}{7} + \frac{\sin^{6}{\left(x \right)} \cos{\left(x \right)}}{7} + \frac{2 \sin^{4}{\left(x \right)} \cos^{3}{\left(x \right)}}{7} + \frac{8 \sin^{2}{\left(x \right)} \cos^{5}{\left(x \right)}}{35} + \frac{16 \cos^{7}{\left(x \right)}}{245}$$
Gráfica
Respuesta
[src]
7 7 6 3 4 5 2 16 sin (1) 16*cos (1) sin (1)*cos(1) 2*cos (1)*sin (1) 8*cos (1)*sin (1) - --- + ------- + ---------- + -------------- + ----------------- + ----------------- 245 7 245 7 7 35
$$- \frac{16}{245} + \frac{16 \cos^{7}{\left(1 \right)}}{245} + \frac{8 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{35} + \frac{2 \sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{7} + \frac{\sin^{6}{\left(1 \right)} \cos{\left(1 \right)}}{7} + \frac{\sin^{7}{\left(1 \right)}}{7}$$
=
=
7 7 6 3 4 5 2 16 sin (1) 16*cos (1) sin (1)*cos(1) 2*cos (1)*sin (1) 8*cos (1)*sin (1) - --- + ------- + ---------- + -------------- + ----------------- + ----------------- 245 7 245 7 7 35
$$- \frac{16}{245} + \frac{16 \cos^{7}{\left(1 \right)}}{245} + \frac{8 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{35} + \frac{2 \sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{7} + \frac{\sin^{6}{\left(1 \right)} \cos{\left(1 \right)}}{7} + \frac{\sin^{7}{\left(1 \right)}}{7}$$
-16/245 + sin(1)^7/7 + 16*cos(1)^7/245 + sin(1)^6*cos(1)/7 + 2*cos(1)^3*sin(1)^4/7 + 8*cos(1)^5*sin(1)^2/35
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.