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