Sr Examen
Integral de sin^4(3x/2)*cos^2(3x/2) dx
Solución
Ha introducido
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1 / | | 4/3*x\ 2/3*x\ | sin |---|*cos |---| dx | \ 2 / \ 2 / | / 0
$$\int\limits_{0}^{1} \sin^{4}{\left(\frac{3 x}{2} \right)} \cos^{2}{\left(\frac{3 x}{2} \right)}\, dx$$
Integral(sin((3*x)/2)^4*cos((3*x)/2)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ /3*x\ /3*x\ 3/3*x\ /3*x\ 5/3*x\ /3*x\ | cos|---|*sin|---| sin |---|*cos|---| sin |---|*cos|---| | 4/3*x\ 2/3*x\ x \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / | sin |---|*cos |---| dx = C + -- - ----------------- - ------------------ + ------------------ | \ 2 / \ 2 / 16 24 36 9 | /
$$\int \sin^{4}{\left(\frac{3 x}{2} \right)} \cos^{2}{\left(\frac{3 x}{2} \right)}\, dx = C + \frac{x}{16} + \frac{\sin^{5}{\left(\frac{3 x}{2} \right)} \cos{\left(\frac{3 x}{2} \right)}}{9} - \frac{\sin^{3}{\left(\frac{3 x}{2} \right)} \cos{\left(\frac{3 x}{2} \right)}}{36} - \frac{\sin{\left(\frac{3 x}{2} \right)} \cos{\left(\frac{3 x}{2} \right)}}{24}$$
Gráfica
Respuesta
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3 5 1 cos(3/2)*sin(3/2) sin (3/2)*cos(3/2) sin (3/2)*cos(3/2) -- - ----------------- - ------------------ + ------------------ 16 24 36 9
$$- \frac{\sin{\left(\frac{3}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{24} - \frac{\sin^{3}{\left(\frac{3}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{36} + \frac{\sin^{5}{\left(\frac{3}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{9} + \frac{1}{16}$$
=
=
3 5 1 cos(3/2)*sin(3/2) sin (3/2)*cos(3/2) sin (3/2)*cos(3/2) -- - ----------------- - ------------------ + ------------------ 16 24 36 9
$$- \frac{\sin{\left(\frac{3}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{24} - \frac{\sin^{3}{\left(\frac{3}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{36} + \frac{\sin^{5}{\left(\frac{3}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{9} + \frac{1}{16}$$
1/16 - cos(3/2)*sin(3/2)/24 - sin(3/2)^3*cos(3/2)/36 + sin(3/2)^5*cos(3/2)/9
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.