Sr Examen
Integral de cos(x/2)^3*sin(x) dx
Solución
Ha introducido
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1 / | | 3/x\ | cos |-|*sin(x) dx | \2/ | / 0
$$\int\limits_{0}^{1} \sin{\left(x \right)} \cos^{3}{\left(\frac{x}{2} \right)}\, dx$$
Integral(cos(x/2)^3*sin(x), (x, 0, 1))
Respuesta
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3 3 2 2 4 4*cos (1/2)*cos(1) 4*sin (1/2)*sin(1) 8*sin (1/2)*cos(1)*cos(1/2) 2*cos (1/2)*sin(1)*sin(1/2) - - ------------------ - ------------------ - --------------------------- + --------------------------- 5 5 5 5 5
$$- \frac{4 \cos^{3}{\left(\frac{1}{2} \right)} \cos{\left(1 \right)}}{5} - \frac{8 \sin^{2}{\left(\frac{1}{2} \right)} \cos{\left(\frac{1}{2} \right)} \cos{\left(1 \right)}}{5} - \frac{4 \sin^{3}{\left(\frac{1}{2} \right)} \sin{\left(1 \right)}}{5} + \frac{2 \sin{\left(\frac{1}{2} \right)} \sin{\left(1 \right)} \cos^{2}{\left(\frac{1}{2} \right)}}{5} + \frac{4}{5}$$
=
=
3 3 2 2 4 4*cos (1/2)*cos(1) 4*sin (1/2)*sin(1) 8*sin (1/2)*cos(1)*cos(1/2) 2*cos (1/2)*sin(1)*sin(1/2) - - ------------------ - ------------------ - --------------------------- + --------------------------- 5 5 5 5 5
$$- \frac{4 \cos^{3}{\left(\frac{1}{2} \right)} \cos{\left(1 \right)}}{5} - \frac{8 \sin^{2}{\left(\frac{1}{2} \right)} \cos{\left(\frac{1}{2} \right)} \cos{\left(1 \right)}}{5} - \frac{4 \sin^{3}{\left(\frac{1}{2} \right)} \sin{\left(1 \right)}}{5} + \frac{2 \sin{\left(\frac{1}{2} \right)} \sin{\left(1 \right)} \cos^{2}{\left(\frac{1}{2} \right)}}{5} + \frac{4}{5}$$
4/5 - 4*cos(1/2)^3*cos(1)/5 - 4*sin(1/2)^3*sin(1)/5 - 8*sin(1/2)^2*cos(1)*cos(1/2)/5 + 2*cos(1/2)^2*sin(1)*sin(1/2)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.