Sr Examen
Integral de cosx^3*2*x dx
Solución
Ha introducido
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1/2 / | | 3 | cos (x)*2*x dx | / 0
$$\int\limits_{0}^{\frac{1}{2}} x 2 \cos^{3}{\left(x \right)}\, dx$$
Integral((cos(x)^3*2)*x, (x, 0, 1/2))
Respuesta (Indefinida)
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/ | 3 3 2 | 3 14*cos (x) 4*x*sin (x) 4*sin (x)*cos(x) 2 | cos (x)*2*x dx = C + ---------- + ----------- + ---------------- + 2*x*cos (x)*sin(x) | 9 3 3 /
$$\int x 2 \cos^{3}{\left(x \right)}\, dx = C + \frac{4 x \sin^{3}{\left(x \right)}}{3} + 2 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{4 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{3} + \frac{14 \cos^{3}{\left(x \right)}}{9}$$
Gráfica
Respuesta
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3 3 2 14 2*sin (1/2) 14*cos (1/2) 2 4*sin (1/2)*cos(1/2) - -- + ----------- + ------------ + cos (1/2)*sin(1/2) + -------------------- 9 3 9 3
$$- \frac{14}{9} + \frac{2 \sin^{3}{\left(\frac{1}{2} \right)}}{3} + \frac{4 \sin^{2}{\left(\frac{1}{2} \right)} \cos{\left(\frac{1}{2} \right)}}{3} + \sin{\left(\frac{1}{2} \right)} \cos^{2}{\left(\frac{1}{2} \right)} + \frac{14 \cos^{3}{\left(\frac{1}{2} \right)}}{9}$$
=
=
3 3 2 14 2*sin (1/2) 14*cos (1/2) 2 4*sin (1/2)*cos(1/2) - -- + ----------- + ------------ + cos (1/2)*sin(1/2) + -------------------- 9 3 9 3
$$- \frac{14}{9} + \frac{2 \sin^{3}{\left(\frac{1}{2} \right)}}{3} + \frac{4 \sin^{2}{\left(\frac{1}{2} \right)} \cos{\left(\frac{1}{2} \right)}}{3} + \sin{\left(\frac{1}{2} \right)} \cos^{2}{\left(\frac{1}{2} \right)} + \frac{14 \cos^{3}{\left(\frac{1}{2} \right)}}{9}$$
-14/9 + 2*sin(1/2)^3/3 + 14*cos(1/2)^3/9 + cos(1/2)^2*sin(1/2) + 4*sin(1/2)^2*cos(1/2)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.