Sr Examen
Integral de x*sin(4x)^2 dx
Solución
Ha introducido
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1 / | | 2 | x*sin (4*x) dx | / 0
$$\int\limits_{0}^{1} x \sin^{2}{\left(4 x \right)}\, dx$$
Integral(x*sin(4*x)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ | 2 2 2 2 2 | 2 cos (4*x) x *cos (4*x) x *sin (4*x) x*cos(4*x)*sin(4*x) | x*sin (4*x) dx = C - --------- + ------------ + ------------ - ------------------- | 64 4 4 8 /
$$\int x \sin^{2}{\left(4 x \right)}\, dx = C + \frac{x^{2} \sin^{2}{\left(4 x \right)}}{4} + \frac{x^{2} \cos^{2}{\left(4 x \right)}}{4} - \frac{x \sin{\left(4 x \right)} \cos{\left(4 x \right)}}{8} - \frac{\cos^{2}{\left(4 x \right)}}{64}$$
Gráfica
Respuesta
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2 2 cos (4) 17*sin (4) cos(4)*sin(4) ------- + ---------- - ------------- 4 64 8
$$- \frac{\sin{\left(4 \right)} \cos{\left(4 \right)}}{8} + \frac{\cos^{2}{\left(4 \right)}}{4} + \frac{17 \sin^{2}{\left(4 \right)}}{64}$$
=
=
2 2 cos (4) 17*sin (4) cos(4)*sin(4) ------- + ---------- - ------------- 4 64 8
$$- \frac{\sin{\left(4 \right)} \cos{\left(4 \right)}}{8} + \frac{\cos^{2}{\left(4 \right)}}{4} + \frac{17 \sin^{2}{\left(4 \right)}}{64}$$
cos(4)^2/4 + 17*sin(4)^2/64 - cos(4)*sin(4)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.