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