Sr Examen
Integral de x^2*cos(x)^3 dx
Solución
Ha introducido
[src]
1 / | | 2 3 | x *cos (x) dx | / 0
$$\int\limits_{0}^{1} x^{2} \cos^{3}{\left(x \right)}\, dx$$
Integral(x^2*cos(x)^3, (x, 0, 1))
Respuesta (Indefinida)
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/ | 3 2 2 3 3 2 | 2 3 40*sin (x) 14*cos (x)*sin(x) 2*x *sin (x) 14*x*cos (x) 2 2 4*x*sin (x)*cos(x) | x *cos (x) dx = C - ---------- - ----------------- + ------------ + ------------ + x *cos (x)*sin(x) + ------------------ | 27 9 3 9 3 /
$$\int x^{2} \cos^{3}{\left(x \right)}\, dx = C + \frac{2 x^{2} \sin^{3}{\left(x \right)}}{3} + x^{2} \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{4 x \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{3} + \frac{14 x \cos^{3}{\left(x \right)}}{9} - \frac{40 \sin^{3}{\left(x \right)}}{27} - \frac{14 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{9}$$
Gráfica
Respuesta
[src]
3 3 2 2
22*sin (1) 14*cos (1) 5*cos (1)*sin(1) 4*sin (1)*cos(1)
- ---------- + ---------- - ---------------- + ----------------
27 9 9 3
$$- \frac{22 \sin^{3}{\left(1 \right)}}{27} - \frac{5 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{9} + \frac{14 \cos^{3}{\left(1 \right)}}{9} + \frac{4 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{3}$$
=
=
3 3 2 2
22*sin (1) 14*cos (1) 5*cos (1)*sin(1) 4*sin (1)*cos(1)
- ---------- + ---------- - ---------------- + ----------------
27 9 9 3
$$- \frac{22 \sin^{3}{\left(1 \right)}}{27} - \frac{5 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{9} + \frac{14 \cos^{3}{\left(1 \right)}}{9} + \frac{4 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{3}$$
-22*sin(1)^3/27 + 14*cos(1)^3/9 - 5*cos(1)^2*sin(1)/9 + 4*sin(1)^2*cos(1)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.