Sr Examen
Integral de sin(2*x+1)*(cos((x-3)/2)^2) dx
Solución
Ha introducido
[src]
1 / | | 2/x - 3\ | sin(2*x + 1)*cos |-----| dx | \ 2 / | / 0
$$\int\limits_{0}^{1} \sin{\left(2 x + 1 \right)} \cos^{2}{\left(\frac{x - 3}{2} \right)}\, dx$$
Integral(sin(2*x + 1)*cos((x - 3)/2)^2, (x, 0, 1))
Gráfica
Respuesta
[src]
2 2 2 2
7*cos (1)*cos(3) sin (3/2)*cos(1) sin (1)*cos(3) 7*cos (3/2)*cos(1) cos(3/2)*sin(1)*sin(3/2) cos(1)*sin(1)*sin(3)
- ---------------- - ---------------- + -------------- + ------------------ - ------------------------ + --------------------
12 12 12 12 3 3
$$\frac{\sin^{2}{\left(1 \right)} \cos{\left(3 \right)}}{12} - \frac{\sin^{2}{\left(\frac{3}{2} \right)} \cos{\left(1 \right)}}{12} - \frac{\sin{\left(1 \right)} \sin{\left(\frac{3}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{3} + \frac{7 \cos{\left(1 \right)} \cos^{2}{\left(\frac{3}{2} \right)}}{12} + \frac{\sin{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{3} - \frac{7 \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{12}$$
=
=
2 2 2 2
7*cos (1)*cos(3) sin (3/2)*cos(1) sin (1)*cos(3) 7*cos (3/2)*cos(1) cos(3/2)*sin(1)*sin(3/2) cos(1)*sin(1)*sin(3)
- ---------------- - ---------------- + -------------- + ------------------ - ------------------------ + --------------------
12 12 12 12 3 3
$$\frac{\sin^{2}{\left(1 \right)} \cos{\left(3 \right)}}{12} - \frac{\sin^{2}{\left(\frac{3}{2} \right)} \cos{\left(1 \right)}}{12} - \frac{\sin{\left(1 \right)} \sin{\left(\frac{3}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{3} + \frac{7 \cos{\left(1 \right)} \cos^{2}{\left(\frac{3}{2} \right)}}{12} + \frac{\sin{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{3} - \frac{7 \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{12}$$
-7*cos(1)^2*cos(3)/12 - sin(3/2)^2*cos(1)/12 + sin(1)^2*cos(3)/12 + 7*cos(3/2)^2*cos(1)/12 - cos(3/2)*sin(1)*sin(3/2)/3 + cos(1)*sin(1)*sin(3)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.