Sr Examen
Integral de 8*sin^2(x)*cos^4(x) dx
Solución
Ha introducido
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1 / | | 2 4 | 8*sin (x)*cos (x) dx | / 0
$$\int\limits_{0}^{1} 8 \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}\, dx$$
Integral((8*sin(x)^2)*cos(x)^4, (x, 0, 1))
Respuesta (Indefinida)
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/ | 6 6 5 5 3 3 2 4 4 2 | 2 4 x*cos (x) x*sin (x) sin (x)*cos(x) cos (x)*sin(x) 4*cos (x)*sin (x) 3*x*cos (x)*sin (x) 3*x*cos (x)*sin (x) | 8*sin (x)*cos (x) dx = C + --------- + --------- + -------------- - -------------- + ----------------- + ------------------- + ------------------- | 2 2 2 2 3 2 2 /
$$\int 8 \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}\, dx = C + \frac{x \sin^{6}{\left(x \right)}}{2} + \frac{3 x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{3 x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{2} + \frac{x \cos^{6}{\left(x \right)}}{2} + \frac{\sin^{5}{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{4 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} - \frac{\sin{\left(x \right)} \cos^{5}{\left(x \right)}}{2}$$
Gráfica
Respuesta
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5 3 1 cos(1)*sin(1) 4*cos (1)*sin(1) cos (1)*sin(1) - + ------------- - ---------------- + -------------- 2 2 3 3
$$- \frac{4 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{3} + \frac{\sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{3} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{1}{2}$$
=
=
5 3 1 cos(1)*sin(1) 4*cos (1)*sin(1) cos (1)*sin(1) - + ------------- - ---------------- + -------------- 2 2 3 3
$$- \frac{4 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{3} + \frac{\sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{3} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{1}{2}$$
1/2 + cos(1)*sin(1)/2 - 4*cos(1)^5*sin(1)/3 + cos(1)^3*sin(1)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.