Sr Examen
Integral de -9*3*4*cos(x)^2*sin(x)^4 dx
Solución
Ha introducido
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0 / | | 2 4 | -108*cos (x)*sin (x) dx | / pi -- 2
$$\int\limits_{\frac{\pi}{2}}^{0} \sin^{4}{\left(x \right)} \left(- 108 \cos^{2}{\left(x \right)}\right)\, dx$$
Integral((-108*cos(x)^2)*sin(x)^4, (x, pi/2, 0))
Respuesta (Indefinida)
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/ | 6 6 5 5 2 4 4 2 | 2 4 3 3 27*x*cos (x) 27*x*sin (x) 27*sin (x)*cos(x) 27*cos (x)*sin(x) 81*x*cos (x)*sin (x) 81*x*cos (x)*sin (x) | -108*cos (x)*sin (x) dx = C + 18*cos (x)*sin (x) - ------------ - ------------ - ----------------- + ----------------- - -------------------- - -------------------- | 4 4 4 4 4 4 /
$$\int \sin^{4}{\left(x \right)} \left(- 108 \cos^{2}{\left(x \right)}\right)\, dx = C - \frac{27 x \sin^{6}{\left(x \right)}}{4} - \frac{81 x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} - \frac{81 x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} - \frac{27 x \cos^{6}{\left(x \right)}}{4} - \frac{27 \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{4} + 18 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)} + \frac{27 \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{4}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.