Sr Examen
Integral de (sin^2)2xcos3xdx dx
Solución
Ha introducido
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1 / | | 2 | sin (x)*2*x*cos(3*x) dx | / 0
$$\int\limits_{0}^{1} x 2 \sin^{2}{\left(x \right)} \cos{\left(3 x \right)}\, dx$$
Integral(((sin(x)^2*2)*x)*cos(3*x), (x, 0, 1))
Respuesta (Indefinida)
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/ | 3 5 5 4 3 2 2 3 | 2 4*cos (x) 208*cos (x) 3 2 16*x*sin (x) 16*sin (x)*cos(x) 104*cos (x)*sin (x) 8*x*cos (x)*sin (x) | sin (x)*2*x*cos(3*x) dx = C - --------- + ----------- - 2*x*sin (x) - 2*sin (x)*cos(x) + ------------ + ----------------- + ------------------- + ------------------- | 3 225 15 15 45 3 /
$$\int x 2 \sin^{2}{\left(x \right)} \cos{\left(3 x \right)}\, dx = C + \frac{16 x \sin^{5}{\left(x \right)}}{15} + \frac{8 x \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{3} - 2 x \sin^{3}{\left(x \right)} + \frac{16 \sin^{4}{\left(x \right)} \cos{\left(x \right)}}{15} + \frac{104 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{45} - 2 \sin^{2}{\left(x \right)} \cos{\left(x \right)} + \frac{208 \cos^{5}{\left(x \right)}}{225} - \frac{4 \cos^{3}{\left(x \right)}}{3}$$
Gráfica
Respuesta
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2 2 2 2 92 92*cos (1)*cos(3) 4*cos (1)*sin(3) 14*sin (1)*sin(3) 142*sin (1)*cos(3) 24*cos(1)*sin(1)*sin(3) 4*cos(1)*cos(3)*sin(1) --- - ----------------- - ---------------- + ----------------- + ------------------ - ----------------------- + ---------------------- 225 225 15 15 225 25 5
$$\frac{142 \sin^{2}{\left(1 \right)} \cos{\left(3 \right)}}{225} + \frac{4 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{5} - \frac{24 \sin{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{25} - \frac{4 \sin{\left(3 \right)} \cos^{2}{\left(1 \right)}}{15} + \frac{14 \sin^{2}{\left(1 \right)} \sin{\left(3 \right)}}{15} - \frac{92 \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{225} + \frac{92}{225}$$
=
=
2 2 2 2 92 92*cos (1)*cos(3) 4*cos (1)*sin(3) 14*sin (1)*sin(3) 142*sin (1)*cos(3) 24*cos(1)*sin(1)*sin(3) 4*cos(1)*cos(3)*sin(1) --- - ----------------- - ---------------- + ----------------- + ------------------ - ----------------------- + ---------------------- 225 225 15 15 225 25 5
$$\frac{142 \sin^{2}{\left(1 \right)} \cos{\left(3 \right)}}{225} + \frac{4 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{5} - \frac{24 \sin{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{25} - \frac{4 \sin{\left(3 \right)} \cos^{2}{\left(1 \right)}}{15} + \frac{14 \sin^{2}{\left(1 \right)} \sin{\left(3 \right)}}{15} - \frac{92 \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{225} + \frac{92}{225}$$
92/225 - 92*cos(1)^2*cos(3)/225 - 4*cos(1)^2*sin(3)/15 + 14*sin(1)^2*sin(3)/15 + 142*sin(1)^2*cos(3)/225 - 24*cos(1)*sin(1)*sin(3)/25 + 4*cos(1)*cos(3)*sin(1)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.