Sr Examen
Integral de (sin^3)xcosx dx
Solución
Ha introducido
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1 / | | 3 | sin (x)*x*cos(x) dx | / 0
$$\int\limits_{0}^{1} x \sin^{3}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral((sin(x)^3*x)*cos(x), (x, 0, 1))
Respuesta (Indefinida)
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/ | 4 3 4 3 2 2 | 3 3*x*cos (x) 3*cos (x)*sin(x) 5*x*sin (x) 5*sin (x)*cos(x) 3*x*cos (x)*sin (x) | sin (x)*x*cos(x) dx = C - ----------- + ---------------- + ----------- + ---------------- - ------------------- | 32 32 32 32 16 /
$$\int x \sin^{3}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{5 x \sin^{4}{\left(x \right)}}{32} - \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} - \frac{3 x \cos^{4}{\left(x \right)}}{32} + \frac{5 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{32} + \frac{3 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{32}$$
Gráfica
Respuesta
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4 4 2 2 3 3
3*cos (1) 5*sin (1) 3*cos (1)*sin (1) 3*cos (1)*sin(1) 5*sin (1)*cos(1)
- --------- + --------- - ----------------- + ---------------- + ----------------
32 32 16 32 32
$$- \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{16} - \frac{3 \cos^{4}{\left(1 \right)}}{32} + \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{32} + \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{32} + \frac{5 \sin^{4}{\left(1 \right)}}{32}$$
=
=
4 4 2 2 3 3
3*cos (1) 5*sin (1) 3*cos (1)*sin (1) 3*cos (1)*sin(1) 5*sin (1)*cos(1)
- --------- + --------- - ----------------- + ---------------- + ----------------
32 32 16 32 32
$$- \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{16} - \frac{3 \cos^{4}{\left(1 \right)}}{32} + \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{32} + \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{32} + \frac{5 \sin^{4}{\left(1 \right)}}{32}$$
-3*cos(1)^4/32 + 5*sin(1)^4/32 - 3*cos(1)^2*sin(1)^2/16 + 3*cos(1)^3*sin(1)/32 + 5*sin(1)^3*cos(1)/32
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.