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