Sr Examen
Integral de (2^8)(sin^2x)(cos^6x) dx
Solución
Ha introducido
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0 / | | 2 6 | 256*sin (x)*cos (x) dx | / -pi ---- 2
$$\int\limits_{- \frac{\pi}{2}}^{0} 256 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}\, dx$$
Integral((256*sin(x)^2)*cos(x)^6, (x, -pi/2, 0))
Respuesta (Indefinida)
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/ | 3 5 5 3 | 2 6 7 8 8 7 110*cos (x)*sin (x) 146*cos (x)*sin (x) 2 6 6 2 4 4 | 256*sin (x)*cos (x) dx = C - 10*cos (x)*sin(x) + 10*x*cos (x) + 10*x*sin (x) + 10*sin (x)*cos(x) + ------------------- + ------------------- + 40*x*cos (x)*sin (x) + 40*x*cos (x)*sin (x) + 60*x*cos (x)*sin (x) | 3 3 /
$$\int 256 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}\, dx = C + 10 x \sin^{8}{\left(x \right)} + 40 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)} + 60 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)} + 40 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)} + 10 x \cos^{8}{\left(x \right)} + 10 \sin^{7}{\left(x \right)} \cos{\left(x \right)} + \frac{110 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} + \frac{146 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{3} - 10 \sin{\left(x \right)} \cos^{7}{\left(x \right)}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.