Sr Examen
Integral de 2^8*sin(x)^4*cos(x)^4 dx
Solución
Ha introducido
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0 / | | 4 4 | 256*sin (x)*cos (x) dx | / -p --- 2
$$\int\limits_{- \frac{p}{2}}^{0} 256 \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}\, dx$$
Integral((256*sin(x)^4)*cos(x)^4, (x, -p/2, 0))
Respuesta (Indefinida)
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/ | | 4 4 5 3 7 8 8 7 3 5 2 6 6 2 4 4 | 256*sin (x)*cos (x) dx = C - 22*cos (x)*sin (x) - 6*cos (x)*sin(x) + 6*x*cos (x) + 6*x*sin (x) + 6*sin (x)*cos(x) + 22*cos (x)*sin (x) + 24*x*cos (x)*sin (x) + 24*x*cos (x)*sin (x) + 36*x*cos (x)*sin (x) | /
$$\int 256 \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}\, dx = C + 6 x \sin^{8}{\left(x \right)} + 24 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)} + 36 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)} + 24 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)} + 6 x \cos^{8}{\left(x \right)} + 6 \sin^{7}{\left(x \right)} \cos{\left(x \right)} + 22 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)} - 22 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)} - 6 \sin{\left(x \right)} \cos^{7}{\left(x \right)}$$
Respuesta
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3 3*p - 3*cos(p)*sin(p) - 2*sin (p)*cos(p)
$$3 p - 2 \sin^{3}{\left(p \right)} \cos{\left(p \right)} - 3 \sin{\left(p \right)} \cos{\left(p \right)}$$
=
=
3 3*p - 3*cos(p)*sin(p) - 2*sin (p)*cos(p)
$$3 p - 2 \sin^{3}{\left(p \right)} \cos{\left(p \right)} - 3 \sin{\left(p \right)} \cos{\left(p \right)}$$
3*p - 3*cos(p)*sin(p) - 2*sin(p)^3*cos(p)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.