Sr Examen
Integral de abs((4+2*sin(0,1x)+3*x^2*sin(1,2*x))) dx
Solución
Ha introducido
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5 / | | | /x \ 2 /6*x\| | |4 + 2*sin|--| + 3*x *sin|---|| dx | | \10/ \ 5 /| | / 1
$$\int\limits_{1}^{5} \left|{3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + \left(2 \sin{\left(\frac{x}{10} \right)} + 4\right)}\right|\, dx$$
Integral(Abs(4 + 2*sin(x/10) + (3*x^2)*sin(6*x/5)), (x, 1, 5))
Respuesta
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5 / | | / /x \ 2 /6*x\ /x \ 2 /6*x\ | |4 + 2*sin|--| + 3*x *sin|---| for 4 + 2*sin|--| + 3*x *sin|---| >= 0 | | \10/ \ 5 / \10/ \ 5 / | < dx | | /x \ 2 /6*x\ | |-4 - 2*sin|--| - 3*x *sin|---| otherwise | \ \10/ \ 5 / | / 1
$$\int\limits_{1}^{5} \begin{cases} 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + 2 \sin{\left(\frac{x}{10} \right)} + 4 & \text{for}\: 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + 2 \sin{\left(\frac{x}{10} \right)} + 4 \geq 0 \\- 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} - 2 \sin{\left(\frac{x}{10} \right)} - 4 & \text{otherwise} \end{cases}\, dx$$
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5 / | | / /x \ 2 /6*x\ /x \ 2 /6*x\ | |4 + 2*sin|--| + 3*x *sin|---| for 4 + 2*sin|--| + 3*x *sin|---| >= 0 | | \10/ \ 5 / \10/ \ 5 / | < dx | | /x \ 2 /6*x\ | |-4 - 2*sin|--| - 3*x *sin|---| otherwise | \ \10/ \ 5 / | / 1
$$\int\limits_{1}^{5} \begin{cases} 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + 2 \sin{\left(\frac{x}{10} \right)} + 4 & \text{for}\: 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} + 2 \sin{\left(\frac{x}{10} \right)} + 4 \geq 0 \\- 3 x^{2} \sin{\left(\frac{6 x}{5} \right)} - 2 \sin{\left(\frac{x}{10} \right)} - 4 & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((4 + 2*sin(x/10) + 3*x^2*sin(6*x/5), 4 + 2*sin(x/10) + 3*x^2*sin(6*x/5) >= 0), (-4 - 2*sin(x/10) - 3*x^2*sin(6*x/5), True)), (x, 1, 5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.