Sr Examen
Integral de x^3×cos(x)^4 dx
Solución
Ha introducido
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1 / | | 3 4 | x *cos (x) dx | / 0
$$\int\limits_{0}^{1} x^{3} \cos^{4}{\left(x \right)}\, dx$$
Integral(x^3*cos(x)^4, (x, 0, 1))
Respuesta (Indefinida)
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/ | 4 4 2 4 4 4 4 4 2 4 3 3 2 2 2 3 3 4 2 2 3 3 | 3 4 51*cos (x) 45*sin (x) 45*x *sin (x) 3*x *cos (x) 3*x *sin (x) 51*x *cos (x) 51*x*cos (x)*sin(x) 45*x*sin (x)*cos(x) 9*x *cos (x)*sin (x) 3*x *sin (x)*cos(x) 3*x *cos (x)*sin (x) 5*x *cos (x)*sin(x) | x *cos (x) dx = C - ---------- + ---------- - ------------- + ------------ + ------------ + ------------- - ------------------- - ------------------- - -------------------- + ------------------- + -------------------- + ------------------- | 256 256 128 32 32 128 64 64 64 8 16 8 /
$$\int x^{3} \cos^{4}{\left(x \right)}\, dx = C + \frac{3 x^{4} \sin^{4}{\left(x \right)}}{32} + \frac{3 x^{4} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} + \frac{3 x^{4} \cos^{4}{\left(x \right)}}{32} + \frac{3 x^{3} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{5 x^{3} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{45 x^{2} \sin^{4}{\left(x \right)}}{128} - \frac{9 x^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{64} + \frac{51 x^{2} \cos^{4}{\left(x \right)}}{128} - \frac{45 x \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{64} - \frac{51 x \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{64} + \frac{45 \sin^{4}{\left(x \right)}}{256} - \frac{51 \cos^{4}{\left(x \right)}}{256}$$
Gráfica
Respuesta
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4 4 3 3 2 2 51 21*sin (1) 75*cos (1) 21*sin (1)*cos(1) 11*cos (1)*sin(1) 3*cos (1)*sin (1) --- - ---------- + ---------- - ----------------- - ----------------- + ----------------- 256 256 256 64 64 64
$$- \frac{21 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{64} - \frac{21 \sin^{4}{\left(1 \right)}}{256} - \frac{11 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{64} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{64} + \frac{75 \cos^{4}{\left(1 \right)}}{256} + \frac{51}{256}$$
=
=
4 4 3 3 2 2 51 21*sin (1) 75*cos (1) 21*sin (1)*cos(1) 11*cos (1)*sin(1) 3*cos (1)*sin (1) --- - ---------- + ---------- - ----------------- - ----------------- + ----------------- 256 256 256 64 64 64
$$- \frac{21 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{64} - \frac{21 \sin^{4}{\left(1 \right)}}{256} - \frac{11 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{64} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{64} + \frac{75 \cos^{4}{\left(1 \right)}}{256} + \frac{51}{256}$$
51/256 - 21*sin(1)^4/256 + 75*cos(1)^4/256 - 21*sin(1)^3*cos(1)/64 - 11*cos(1)^3*sin(1)/64 + 3*cos(1)^2*sin(1)^2/64
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.