Sr Examen
Integral de 2*cos(x)^3*3*Abs(sin(2*x)) dx
Solución
Ha introducido
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1 / | | 3 | 2*cos (x)*3*|sin(2*x)| dx | / 0
$$\int\limits_{0}^{1} 3 \cdot 2 \cos^{3}{\left(x \right)} \left|{\sin{\left(2 x \right)}}\right|\, dx$$
Integral(((2*cos(x)^3)*3)*Abs(sin(2*x)), (x, 0, 1))
Respuesta
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3 3 2 2 12 12*cos (1)*cos(2) 12*sin (1)*sin(2) 24*sin (1)*cos(1)*cos(2) 6*cos (1)*sin(1)*sin(2) -- - ----------------- - ----------------- - ------------------------ + ----------------------- 5 5 5 5 5
$$- \frac{12 \sin^{3}{\left(1 \right)} \sin{\left(2 \right)}}{5} - \frac{12 \cos^{3}{\left(1 \right)} \cos{\left(2 \right)}}{5} + \frac{6 \sin{\left(1 \right)} \sin{\left(2 \right)} \cos^{2}{\left(1 \right)}}{5} - \frac{24 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{5} + \frac{12}{5}$$
=
=
3 3 2 2 12 12*cos (1)*cos(2) 12*sin (1)*sin(2) 24*sin (1)*cos(1)*cos(2) 6*cos (1)*sin(1)*sin(2) -- - ----------------- - ----------------- - ------------------------ + ----------------------- 5 5 5 5 5
$$- \frac{12 \sin^{3}{\left(1 \right)} \sin{\left(2 \right)}}{5} - \frac{12 \cos^{3}{\left(1 \right)} \cos{\left(2 \right)}}{5} + \frac{6 \sin{\left(1 \right)} \sin{\left(2 \right)} \cos^{2}{\left(1 \right)}}{5} - \frac{24 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(2 \right)}}{5} + \frac{12}{5}$$
12/5 - 12*cos(1)^3*cos(2)/5 - 12*sin(1)^3*sin(2)/5 - 24*sin(1)^2*cos(1)*cos(2)/5 + 6*cos(1)^2*sin(1)*sin(2)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.