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