Sr Examen
Integral de ∫(sinx-cosx)⁷dx dx
Solución
Ha introducido
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1 / | | 7 | (sin(x) - cos(x)) dx | / 0
$$\int\limits_{0}^{1} \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{7}\, dx$$
Integral((sin(x) - cos(x))^7, (x, 0, 1))
Gráfica
Respuesta
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7 7 2 5 5 2 177 177*cos (1) 177*sin (1) 6 6 3 4 4 3 71*cos (1)*sin (1) 71*cos (1)*sin (1) --- - ----------- - ----------- - cos (1)*sin(1) - sin (1)*cos(1) - 9*cos (1)*sin (1) - 9*cos (1)*sin (1) - ------------------ - ------------------ 35 35 35 5 5
$$- \frac{71 \sin^{5}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{5} - \frac{177 \sin^{7}{\left(1 \right)}}{35} - 9 \sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)} - \frac{71 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{5} - 9 \sin^{3}{\left(1 \right)} \cos^{4}{\left(1 \right)} - \sin^{6}{\left(1 \right)} \cos{\left(1 \right)} - \frac{177 \cos^{7}{\left(1 \right)}}{35} - \sin{\left(1 \right)} \cos^{6}{\left(1 \right)} + \frac{177}{35}$$
=
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7 7 2 5 5 2 177 177*cos (1) 177*sin (1) 6 6 3 4 4 3 71*cos (1)*sin (1) 71*cos (1)*sin (1) --- - ----------- - ----------- - cos (1)*sin(1) - sin (1)*cos(1) - 9*cos (1)*sin (1) - 9*cos (1)*sin (1) - ------------------ - ------------------ 35 35 35 5 5
$$- \frac{71 \sin^{5}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{5} - \frac{177 \sin^{7}{\left(1 \right)}}{35} - 9 \sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)} - \frac{71 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{5} - 9 \sin^{3}{\left(1 \right)} \cos^{4}{\left(1 \right)} - \sin^{6}{\left(1 \right)} \cos{\left(1 \right)} - \frac{177 \cos^{7}{\left(1 \right)}}{35} - \sin{\left(1 \right)} \cos^{6}{\left(1 \right)} + \frac{177}{35}$$
177/35 - 177*cos(1)^7/35 - 177*sin(1)^7/35 - cos(1)^6*sin(1) - sin(1)^6*cos(1) - 9*cos(1)^3*sin(1)^4 - 9*cos(1)^4*sin(1)^3 - 71*cos(1)^2*sin(1)^5/5 - 71*cos(1)^5*sin(1)^2/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.