Sr Examen
Integral de xsin^4(x^2)cos^4(x^2) dx
Solución
Ha introducido
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1 / | | 4/ 2\ 4/ 2\ | x*sin \x /*cos \x / dx | / 0
$$\int\limits_{0}^{1} x \sin^{4}{\left(x^{2} \right)} \cos^{4}{\left(x^{2} \right)}\, dx$$
Integral((x*sin(x^2)^4)*cos(x^2)^4, (x, 0, 1))
Respuesta (Indefinida)
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/ | 5/ 2\ 3/ 2\ 7/ 2\ / 2\ 2 8/ 2\ 2 8/ 2\ 7/ 2\ / 2\ 3/ 2\ 5/ 2\ 2 2/ 2\ 6/ 2\ 2 6/ 2\ 2/ 2\ 2 4/ 2\ 4/ 2\ | 4/ 2\ 4/ 2\ 11*cos \x /*sin \x / 3*cos \x /*sin\x / 3*x *cos \x / 3*x *sin \x / 3*sin \x /*cos\x / 11*cos \x /*sin \x / 3*x *cos \x /*sin \x / 3*x *cos \x /*sin \x / 9*x *cos \x /*sin \x / | x*sin \x /*cos \x / dx = C - -------------------- - ------------------ + ------------- + ------------- + ------------------ + -------------------- + ---------------------- + ---------------------- + ---------------------- | 256 256 256 256 256 256 64 64 128 /
$$\int x \sin^{4}{\left(x^{2} \right)} \cos^{4}{\left(x^{2} \right)}\, dx = C + \frac{3 x^{2} \sin^{8}{\left(x^{2} \right)}}{256} + \frac{3 x^{2} \sin^{6}{\left(x^{2} \right)} \cos^{2}{\left(x^{2} \right)}}{64} + \frac{9 x^{2} \sin^{4}{\left(x^{2} \right)} \cos^{4}{\left(x^{2} \right)}}{128} + \frac{3 x^{2} \sin^{2}{\left(x^{2} \right)} \cos^{6}{\left(x^{2} \right)}}{64} + \frac{3 x^{2} \cos^{8}{\left(x^{2} \right)}}{256} + \frac{3 \sin^{7}{\left(x^{2} \right)} \cos{\left(x^{2} \right)}}{256} + \frac{11 \sin^{5}{\left(x^{2} \right)} \cos^{3}{\left(x^{2} \right)}}{256} - \frac{11 \sin^{3}{\left(x^{2} \right)} \cos^{5}{\left(x^{2} \right)}}{256} - \frac{3 \sin{\left(x^{2} \right)} \cos^{7}{\left(x^{2} \right)}}{256}$$
Gráfica
Respuesta
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8 8 5 3 7 2 6 6 2 7 4 4 3 5 3*cos (1) 3*sin (1) 11*cos (1)*sin (1) 3*cos (1)*sin(1) 3*cos (1)*sin (1) 3*cos (1)*sin (1) 3*sin (1)*cos(1) 9*cos (1)*sin (1) 11*cos (1)*sin (1) --------- + --------- - ------------------ - ---------------- + ----------------- + ----------------- + ---------------- + ----------------- + ------------------ 256 256 256 256 64 64 256 128 256
$$- \frac{11 \sin^{3}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{256} - \frac{3 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{256} + \frac{3 \cos^{8}{\left(1 \right)}}{256} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{6}{\left(1 \right)}}{64} + \frac{3 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{256} + \frac{11 \sin^{5}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{256} + \frac{3 \sin^{8}{\left(1 \right)}}{256} + \frac{9 \sin^{4}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{128} + \frac{3 \sin^{6}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{64}$$
=
=
8 8 5 3 7 2 6 6 2 7 4 4 3 5 3*cos (1) 3*sin (1) 11*cos (1)*sin (1) 3*cos (1)*sin(1) 3*cos (1)*sin (1) 3*cos (1)*sin (1) 3*sin (1)*cos(1) 9*cos (1)*sin (1) 11*cos (1)*sin (1) --------- + --------- - ------------------ - ---------------- + ----------------- + ----------------- + ---------------- + ----------------- + ------------------ 256 256 256 256 64 64 256 128 256
$$- \frac{11 \sin^{3}{\left(1 \right)} \cos^{5}{\left(1 \right)}}{256} - \frac{3 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{256} + \frac{3 \cos^{8}{\left(1 \right)}}{256} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{6}{\left(1 \right)}}{64} + \frac{3 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{256} + \frac{11 \sin^{5}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{256} + \frac{3 \sin^{8}{\left(1 \right)}}{256} + \frac{9 \sin^{4}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{128} + \frac{3 \sin^{6}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{64}$$
3*cos(1)^8/256 + 3*sin(1)^8/256 - 11*cos(1)^5*sin(1)^3/256 - 3*cos(1)^7*sin(1)/256 + 3*cos(1)^2*sin(1)^6/64 + 3*cos(1)^6*sin(1)^2/64 + 3*sin(1)^7*cos(1)/256 + 9*cos(1)^4*sin(1)^4/128 + 11*cos(1)^3*sin(1)^5/256
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.