Sr Examen
Integral de (xcos(4x))^(2) dx
Solución
Ha introducido
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1 / | | 2 | (x*cos(4*x)) dx | / 0
$$\int\limits_{0}^{1} \left(x \cos{\left(4 x \right)}\right)^{2}\, dx$$
Integral((x*cos(4*x))^2, (x, 0, 1))
Respuesta (Indefinida)
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/ | 2 3 2 3 2 2 2 | 2 x*sin (4*x) cos(4*x)*sin(4*x) x *cos (4*x) x *sin (4*x) x*cos (4*x) x *cos(4*x)*sin(4*x) | (x*cos(4*x)) dx = C - ----------- - ----------------- + ------------ + ------------ + ----------- + -------------------- | 64 256 6 6 64 8 /
$$\int \left(x \cos{\left(4 x \right)}\right)^{2}\, dx = C + \frac{x^{3} \sin^{2}{\left(4 x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(4 x \right)}}{6} + \frac{x^{2} \sin{\left(4 x \right)} \cos{\left(4 x \right)}}{8} - \frac{x \sin^{2}{\left(4 x \right)}}{64} + \frac{x \cos^{2}{\left(4 x \right)}}{64} - \frac{\sin{\left(4 x \right)} \cos{\left(4 x \right)}}{256}$$
Gráfica
Respuesta
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2 2 29*sin (4) 35*cos (4) 31*cos(4)*sin(4) ---------- + ---------- + ---------------- 192 192 256
$$\frac{31 \sin{\left(4 \right)} \cos{\left(4 \right)}}{256} + \frac{35 \cos^{2}{\left(4 \right)}}{192} + \frac{29 \sin^{2}{\left(4 \right)}}{192}$$
=
=
2 2 29*sin (4) 35*cos (4) 31*cos(4)*sin(4) ---------- + ---------- + ---------------- 192 192 256
$$\frac{31 \sin{\left(4 \right)} \cos{\left(4 \right)}}{256} + \frac{35 \cos^{2}{\left(4 \right)}}{192} + \frac{29 \sin^{2}{\left(4 \right)}}{192}$$
29*sin(4)^2/192 + 35*cos(4)^2/192 + 31*cos(4)*sin(4)/256
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.