Sr Examen
Integral de sqrt((2.5(1-cosx))^2+(2.5sinx)^2) dx
Solución
Ha introducido
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1 / | | _________________________________ | / 2 2 | / /5*(1 - cos(x))\ /5*sin(x)\ | / |--------------| + |--------| dx | \/ \ 2 / \ 2 / | / 0
$$\int\limits_{0}^{1} \sqrt{\left(\frac{5 \left(1 - \cos{\left(x \right)}\right)}{2}\right)^{2} + \left(\frac{5 \sin{\left(x \right)}}{2}\right)^{2}}\, dx$$
Integral(sqrt((5*(1 - cos(x))/2)^2 + (5*sin(x)/2)^2), (x, 0, 1))
Respuesta (Indefinida)
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/
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/ | __________________________________
| | / 2 2
| _________________________________ 5* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
| / 2 2 |
| / /5*(1 - cos(x))\ /5*sin(x)\ /
| / |--------------| + |--------| dx = C + ---------------------------------------------
| \/ \ 2 / \ 2 / 2
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/
$$\int \sqrt{\left(\frac{5 \left(1 - \cos{\left(x \right)}\right)}{2}\right)^{2} + \left(\frac{5 \sin{\left(x \right)}}{2}\right)^{2}}\, dx = C + \frac{5 \int \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx}{2}$$
Respuesta
[src]
1
/
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| __________________________________
| / 2 2
5* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
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/
0
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2
$$\frac{5 \int\limits_{0}^{1} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx}{2}$$
=
=
1
/
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| __________________________________
| / 2 2
5* | \/ 1 + cos (x) + sin (x) - 2*cos(x) dx
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/
0
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2
$$\frac{5 \int\limits_{0}^{1} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} + 1}\, dx}{2}$$
5*Integral(sqrt(1 + cos(x)^2 + sin(x)^2 - 2*cos(x)), (x, 0, 1))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.