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