Sr Examen
Integral de sin(t)^6*(-49)*7*sin(t)^3 dt
Solución
Ha introducido
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7 / | | 6 3 | sin (t)*(-49)*7*sin (t) dt | / 0
$$\int\limits_{0}^{7} 7 \left(-49\right) \sin^{6}{\left(t \right)} \sin^{3}{\left(t \right)}\, dt$$
Integral(((sin(t)^6*(-49))*7)*sin(t)^3, (t, 0, 7))
Respuesta (Indefinida)
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/ | 9 3 6 7 2 5 4 | 6 3 6272*cos (t) 8 2744*cos (t)*sin (t) 3136*cos (t)*sin (t) 5488*cos (t)*sin (t) | sin (t)*(-49)*7*sin (t) dt = C + ------------ + 343*sin (t)*cos(t) + -------------------- + -------------------- + -------------------- | 45 3 5 5 /
$$\int 7 \left(-49\right) \sin^{6}{\left(t \right)} \sin^{3}{\left(t \right)}\, dt = C + 343 \sin^{8}{\left(t \right)} \cos{\left(t \right)} + \frac{2744 \sin^{6}{\left(t \right)} \cos^{3}{\left(t \right)}}{3} + \frac{5488 \sin^{4}{\left(t \right)} \cos^{5}{\left(t \right)}}{5} + \frac{3136 \sin^{2}{\left(t \right)} \cos^{7}{\left(t \right)}}{5} + \frac{6272 \cos^{9}{\left(t \right)}}{45}$$
Gráfica
Respuesta
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3 9 5 6272 7 1372*cos (7) 343*cos (7) 2058*cos (7) - ---- - 196*cos (7) + 343*cos(7) - ------------ + ----------- + ------------ 45 3 9 5
$$- \frac{1372 \cos^{3}{\left(7 \right)}}{3} - \frac{6272}{45} - 196 \cos^{7}{\left(7 \right)} + \frac{343 \cos^{9}{\left(7 \right)}}{9} + \frac{2058 \cos^{5}{\left(7 \right)}}{5} + 343 \cos{\left(7 \right)}$$
=
=
3 9 5 6272 7 1372*cos (7) 343*cos (7) 2058*cos (7) - ---- - 196*cos (7) + 343*cos(7) - ------------ + ----------- + ------------ 45 3 9 5
$$- \frac{1372 \cos^{3}{\left(7 \right)}}{3} - \frac{6272}{45} - 196 \cos^{7}{\left(7 \right)} + \frac{343 \cos^{9}{\left(7 \right)}}{9} + \frac{2058 \cos^{5}{\left(7 \right)}}{5} + 343 \cos{\left(7 \right)}$$
-6272/45 - 196*cos(7)^7 + 343*cos(7) - 1372*cos(7)^3/3 + 343*cos(7)^9/9 + 2058*cos(7)^5/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.