Sr Examen
Integral de (-y^2*sin(y)^3) dy
Solución
Ha introducido
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y / | | 2 3 | -y *sin (y) dy | / 1
$$\int\limits_{1}^{y} - y^{2} \sin^{3}{\left(y \right)}\, dy$$
Integral((-y^2)*sin(y)^3, (y, 1, y))
Respuesta (Indefinida)
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/ | 3 3 2 2 3 2 | 2 3 40*cos (y) 14*y*sin (y) 14*sin (y)*cos(y) 2*y *cos (y) 2 2 4*y*cos (y)*sin(y) | -y *sin (y) dy = C - ---------- - ------------ - ----------------- + ------------ + y *sin (y)*cos(y) - ------------------ | 27 9 9 3 3 /
$$\int - y^{2} \sin^{3}{\left(y \right)}\, dy = C + y^{2} \sin^{2}{\left(y \right)} \cos{\left(y \right)} + \frac{2 y^{2} \cos^{3}{\left(y \right)}}{3} - \frac{14 y \sin^{3}{\left(y \right)}}{9} - \frac{4 y \sin{\left(y \right)} \cos^{2}{\left(y \right)}}{3} - \frac{14 \sin^{2}{\left(y \right)} \cos{\left(y \right)}}{9} - \frac{40 \cos^{3}{\left(y \right)}}{27}$$
Respuesta
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3 3 3 3 2 2 3 2 2 2
40*cos (y) 14*sin (1) 22*cos (1) 14*y*sin (y) 14*sin (y)*cos(y) 2*y *cos (y) 4*cos (1)*sin(1) 5*sin (1)*cos(1) 2 2 4*y*cos (y)*sin(y)
- ---------- + ---------- + ---------- - ------------ - ----------------- + ------------ + ---------------- + ---------------- + y *sin (y)*cos(y) - ------------------
27 9 27 9 9 3 3 9 3
$$y^{2} \sin^{2}{\left(y \right)} \cos{\left(y \right)} + \frac{2 y^{2} \cos^{3}{\left(y \right)}}{3} - \frac{14 y \sin^{3}{\left(y \right)}}{9} - \frac{4 y \sin{\left(y \right)} \cos^{2}{\left(y \right)}}{3} - \frac{14 \sin^{2}{\left(y \right)} \cos{\left(y \right)}}{9} - \frac{40 \cos^{3}{\left(y \right)}}{27} + \frac{22 \cos^{3}{\left(1 \right)}}{27} + \frac{5 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{9} + \frac{4 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \sin^{3}{\left(1 \right)}}{9}$$
=
=
3 3 3 3 2 2 3 2 2 2
40*cos (y) 14*sin (1) 22*cos (1) 14*y*sin (y) 14*sin (y)*cos(y) 2*y *cos (y) 4*cos (1)*sin(1) 5*sin (1)*cos(1) 2 2 4*y*cos (y)*sin(y)
- ---------- + ---------- + ---------- - ------------ - ----------------- + ------------ + ---------------- + ---------------- + y *sin (y)*cos(y) - ------------------
27 9 27 9 9 3 3 9 3
$$y^{2} \sin^{2}{\left(y \right)} \cos{\left(y \right)} + \frac{2 y^{2} \cos^{3}{\left(y \right)}}{3} - \frac{14 y \sin^{3}{\left(y \right)}}{9} - \frac{4 y \sin{\left(y \right)} \cos^{2}{\left(y \right)}}{3} - \frac{14 \sin^{2}{\left(y \right)} \cos{\left(y \right)}}{9} - \frac{40 \cos^{3}{\left(y \right)}}{27} + \frac{22 \cos^{3}{\left(1 \right)}}{27} + \frac{5 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{9} + \frac{4 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)}}{3} + \frac{14 \sin^{3}{\left(1 \right)}}{9}$$
-40*cos(y)^3/27 + 14*sin(1)^3/9 + 22*cos(1)^3/27 - 14*y*sin(y)^3/9 - 14*sin(y)^2*cos(y)/9 + 2*y^2*cos(y)^3/3 + 4*cos(1)^2*sin(1)/3 + 5*sin(1)^2*cos(1)/9 + y^2*sin(y)^2*cos(y) - 4*y*cos(y)^2*sin(y)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.