Sr Examen
Integral de sqrt((-3*sin(x)*cos(x)^2)^2+(3*sin(x)^2*cos(x))^2) dx
Solución
Ha introducido
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157 --- 100 / | | ____________________________________________ | / 2 2 | / / 2 \ / 2 \ | \/ \-3*sin(x)*cos (x)/ + \3*sin (x)*cos(x)/ dx | / 0
$$\int\limits_{0}^{\frac{157}{100}} \sqrt{\left(- 3 \sin{\left(x \right)} \cos^{2}{\left(x \right)}\right)^{2} + \left(3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}\right)^{2}}\, dx$$
Integral(sqrt(((-3*sin(x))*cos(x)^2)^2 + ((3*sin(x)^2)*cos(x))^2), (x, 0, 157/100))
Respuesta
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_______________________
/ 2/157\ 2/157\ 2/157\
3* / cos |---| + sin |---| *sin |---|
\/ \100/ \100/ \100/
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2
$$\frac{3 \sqrt{\cos^{2}{\left(\frac{157}{100} \right)} + \sin^{2}{\left(\frac{157}{100} \right)}} \sin^{2}{\left(\frac{157}{100} \right)}}{2}$$
=
=
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/ 2/157\ 2/157\ 2/157\
3* / cos |---| + sin |---| *sin |---|
\/ \100/ \100/ \100/
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2
$$\frac{3 \sqrt{\cos^{2}{\left(\frac{157}{100} \right)} + \sin^{2}{\left(\frac{157}{100} \right)}} \sin^{2}{\left(\frac{157}{100} \right)}}{2}$$
3*sqrt(cos(157/100)^2 + sin(157/100)^2)*sin(157/100)^2/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.