Sr Examen
Integral de sin(x)^2*cos(x)^5*x dx
Solución
Ha introducido
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1 / | | 2 5 | sin (x)*cos (x)*x dx | / 0
$$\int\limits_{0}^{1} x \sin^{2}{\left(x \right)} \cos^{5}{\left(x \right)}\, dx$$
Integral((sin(x)^2*cos(x)^5)*x, (x, 0, 1))
Respuesta (Indefinida)
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/ | 7 7 6 3 4 5 2 4 3 2 5 | 2 5 818*cos (x) 8*x*sin (x) 8*sin (x)*cos(x) 76*cos (x)*sin (x) 409*cos (x)*sin (x) x*cos (x)*sin (x) 4*x*cos (x)*sin (x) | sin (x)*cos (x)*x dx = C + ----------- + ----------- + ---------------- + ------------------ + ------------------- + ----------------- + ------------------- | 11025 105 105 315 1575 3 15 /
$$\int x \sin^{2}{\left(x \right)} \cos^{5}{\left(x \right)}\, dx = C + \frac{8 x \sin^{7}{\left(x \right)}}{105} + \frac{4 x \sin^{5}{\left(x \right)} \cos^{2}{\left(x \right)}}{15} + \frac{x \sin^{3}{\left(x \right)} \cos^{4}{\left(x \right)}}{3} + \frac{8 \sin^{6}{\left(x \right)} \cos{\left(x \right)}}{105} + \frac{76 \sin^{4}{\left(x \right)} \cos^{3}{\left(x \right)}}{315} + \frac{409 \sin^{2}{\left(x \right)} \cos^{5}{\left(x \right)}}{1575} + \frac{818 \cos^{7}{\left(x \right)}}{11025}$$
Gráfica
Respuesta
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7 7 4 3 2 5 6 3 4 5 2 818 8*sin (1) 818*cos (1) cos (1)*sin (1) 4*cos (1)*sin (1) 8*sin (1)*cos(1) 76*cos (1)*sin (1) 409*cos (1)*sin (1) - ----- + --------- + ----------- + --------------- + ----------------- + ---------------- + ------------------ + ------------------- 11025 105 11025 3 15 105 315 1575
$$- \frac{818}{11025} + \frac{818 \cos^{7}{\left(1 \right)}}{11025} + \frac{409 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{1575} + \frac{8 \sin^{6}{\left(1 \right)} \cos{\left(1 \right)}}{105} + \frac{\sin^{3}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{3} + \frac{76 \sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{315} + \frac{8 \sin^{7}{\left(1 \right)}}{105} + \frac{4 \sin^{5}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{15}$$
=
=
7 7 4 3 2 5 6 3 4 5 2 818 8*sin (1) 818*cos (1) cos (1)*sin (1) 4*cos (1)*sin (1) 8*sin (1)*cos(1) 76*cos (1)*sin (1) 409*cos (1)*sin (1) - ----- + --------- + ----------- + --------------- + ----------------- + ---------------- + ------------------ + ------------------- 11025 105 11025 3 15 105 315 1575
$$- \frac{818}{11025} + \frac{818 \cos^{7}{\left(1 \right)}}{11025} + \frac{409 \sin^{2}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{1575} + \frac{8 \sin^{6}{\left(1 \right)} \cos{\left(1 \right)}}{105} + \frac{\sin^{3}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{3} + \frac{76 \sin^{4}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{315} + \frac{8 \sin^{7}{\left(1 \right)}}{105} + \frac{4 \sin^{5}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{15}$$
-818/11025 + 8*sin(1)^7/105 + 818*cos(1)^7/11025 + cos(1)^4*sin(1)^3/3 + 4*cos(1)^2*sin(1)^5/15 + 8*sin(1)^6*cos(1)/105 + 76*cos(1)^3*sin(1)^4/315 + 409*cos(1)^5*sin(1)^2/1575
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.