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