Sr Examen
Integral de 2^8*sin^2x*cos^6x dx
Solución
Ha introducido
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1 / | | 2 6 | 256*sin (x)*cos (x) dx | / 0
$$\int\limits_{0}^{1} 256 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}\, dx$$
Integral((256*sin(x)^2)*cos(x)^6, (x, 0, 1))
Respuesta (Indefinida)
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/ | 3 5 5 3 | 2 6 7 8 8 7 110*cos (x)*sin (x) 146*cos (x)*sin (x) 2 6 6 2 4 4 | 256*sin (x)*cos (x) dx = C - 10*cos (x)*sin(x) + 10*x*cos (x) + 10*x*sin (x) + 10*sin (x)*cos(x) + ------------------- + ------------------- + 40*x*cos (x)*sin (x) + 40*x*cos (x)*sin (x) + 60*x*cos (x)*sin (x) | 3 3 /
$$\int 256 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}\, dx = C + 10 x \sin^{8}{\left(x \right)} + 40 x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)} + 60 x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)} + 40 x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)} + 10 x \cos^{8}{\left(x \right)} + 10 \sin^{7}{\left(x \right)} \cos{\left(x \right)} + \frac{110 \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} + \frac{146 \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{3} - 10 \sin{\left(x \right)} \cos^{7}{\left(x \right)}$$
Gráfica
Respuesta
[src]
5 3
7 16*cos (1)*sin(1) 20*cos (1)*sin(1)
10 - 32*cos (1)*sin(1) + 10*cos(1)*sin(1) + ----------------- + -----------------
3 3
$$- 32 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)} + \frac{16 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{3} + \frac{20 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{3} + 10 \sin{\left(1 \right)} \cos{\left(1 \right)} + 10$$
=
=
5 3
7 16*cos (1)*sin(1) 20*cos (1)*sin(1)
10 - 32*cos (1)*sin(1) + 10*cos(1)*sin(1) + ----------------- + -----------------
3 3
$$- 32 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)} + \frac{16 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{3} + \frac{20 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{3} + 10 \sin{\left(1 \right)} \cos{\left(1 \right)} + 10$$
10 - 32*cos(1)^7*sin(1) + 10*cos(1)*sin(1) + 16*cos(1)^5*sin(1)/3 + 20*cos(1)^3*sin(1)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.