Sr Examen
Integral de sqrt(3asin(t)(cos(t))^2+3acos(t)(sin(t))^2) dt
Solución
Ha introducido
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2*pi / | | _______________________________________ | / 2 2 | \/ 3*asin(t)*cos (t) + 3*acos(t)*sin (t) dt | / 0
$$\int\limits_{0}^{2 \pi} \sqrt{\sin^{2}{\left(t \right)} 3 \operatorname{acos}{\left(t \right)} + \cos^{2}{\left(t \right)} 3 \operatorname{asin}{\left(t \right)}}\, dt$$
Integral(sqrt((3*asin(t))*cos(t)^2 + (3*acos(t))*sin(t)^2), (t, 0, 2*pi))
Respuesta (Indefinida)
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/ / | | | _______________________________________ | ___________________________________ | / 2 2 ___ | / 2 2 | \/ 3*asin(t)*cos (t) + 3*acos(t)*sin (t) dt = C + \/ 3 * | \/ cos (t)*asin(t) + sin (t)*acos(t) dt | | / /
$$\int \sqrt{\sin^{2}{\left(t \right)} 3 \operatorname{acos}{\left(t \right)} + \cos^{2}{\left(t \right)} 3 \operatorname{asin}{\left(t \right)}}\, dt = C + \sqrt{3} \int \sqrt{\sin^{2}{\left(t \right)} \operatorname{acos}{\left(t \right)} + \cos^{2}{\left(t \right)} \operatorname{asin}{\left(t \right)}}\, dt$$
Respuesta numérica
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(10.5259922957145 + 1.11665341651004j)
(10.5259922957145 + 1.11665341651004j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.