Sr Examen
Integral de 16*cos(x)^4*sin(x)^4 dx
Solución
Ha introducido
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1 / | | 4 4 | 16*cos (x)*sin (x) dx | / 0
$$\int\limits_{0}^{1} \sin^{4}{\left(x \right)} 16 \cos^{4}{\left(x \right)}\, dx$$
Integral((16*cos(x)^4)*sin(x)^4, (x, 0, 1))
Respuesta (Indefinida)
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/ | 5 3 7 8 8 7 3 5 2 6 6 2 4 4 | 4 4 11*cos (x)*sin (x) 3*cos (x)*sin(x) 3*x*cos (x) 3*x*sin (x) 3*sin (x)*cos(x) 11*cos (x)*sin (x) 3*x*cos (x)*sin (x) 3*x*cos (x)*sin (x) 9*x*cos (x)*sin (x) | 16*cos (x)*sin (x) dx = C - ------------------ - ---------------- + ----------- + ----------- + ---------------- + ------------------ + ------------------- + ------------------- + ------------------- | 8 8 8 8 8 8 2 2 4 /
$$\int \sin^{4}{\left(x \right)} 16 \cos^{4}{\left(x \right)}\, dx = C + \frac{3 x \sin^{8}{\left(x \right)}}{8} + \frac{3 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{9 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} + \frac{3 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{2} + \frac{3 x \cos^{8}{\left(x \right)}}{8} + \frac{3 \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{11 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{11 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{8} - \frac{3 \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{8}$$
Gráfica
Respuesta
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3 3 3*cos(2)*sin(2) sin (2)*cos(2) - - --------------- - -------------- 8 16 8
$$- \frac{\sin^{3}{\left(2 \right)} \cos{\left(2 \right)}}{8} - \frac{3 \sin{\left(2 \right)} \cos{\left(2 \right)}}{16} + \frac{3}{8}$$
=
=
3 3 3*cos(2)*sin(2) sin (2)*cos(2) - - --------------- - -------------- 8 16 8
$$- \frac{\sin^{3}{\left(2 \right)} \cos{\left(2 \right)}}{8} - \frac{3 \sin{\left(2 \right)} \cos{\left(2 \right)}}{16} + \frac{3}{8}$$
3/8 - 3*cos(2)*sin(2)/16 - sin(2)^3*cos(2)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.