Sr Examen
Integral de (x^2+0*x+0)*cosx^4 dx
Solución
Ha introducido
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1 / | | / 2 \ 4 | \x + 0*x/*cos (x) dx | / 0
$$\int\limits_{0}^{1} \left(x^{2} + 0 x\right) \cos^{4}{\left(x \right)}\, dx$$
Integral((x^2 + 0*x)*cos(x)^4, (x, 0, 1))
Respuesta (Indefinida)
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/ | 3 4 3 3 4 3 4 4 2 2 3 2 2 2 3 2 3 | / 2 \ 4 17*cos (x)*sin(x) 15*x*sin (x) 15*sin (x)*cos(x) x *cos (x) x *sin (x) 17*x*cos (x) 3*x*cos (x)*sin (x) x *cos (x)*sin (x) 3*x *sin (x)*cos(x) 5*x *cos (x)*sin(x) | \x + 0*x/*cos (x) dx = C - ----------------- - ------------ - ----------------- + ---------- + ---------- + ------------ - ------------------- + ------------------ + ------------------- + ------------------- | 64 64 64 8 8 64 32 4 8 8 /
$$\int \left(x^{2} + 0 x\right) \cos^{4}{\left(x \right)}\, dx = C + \frac{x^{3} \sin^{4}{\left(x \right)}}{8} + \frac{x^{3} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{x^{3} \cos^{4}{\left(x \right)}}{8} + \frac{3 x^{2} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{5 x^{2} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{15 x \sin^{4}{\left(x \right)}}{64} - \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{32} + \frac{17 x \cos^{4}{\left(x \right)}}{64} - \frac{15 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{64} - \frac{17 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{64}$$
Gráfica
Respuesta
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4 4 2 2 3 3
7*sin (1) 25*cos (1) 5*cos (1)*sin (1) 9*sin (1)*cos(1) 23*cos (1)*sin(1)
- --------- + ---------- + ----------------- + ---------------- + -----------------
64 64 32 64 64
$$- \frac{7 \sin^{4}{\left(1 \right)}}{64} + \frac{5 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{32} + \frac{25 \cos^{4}{\left(1 \right)}}{64} + \frac{9 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{64} + \frac{23 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{64}$$
=
=
4 4 2 2 3 3
7*sin (1) 25*cos (1) 5*cos (1)*sin (1) 9*sin (1)*cos(1) 23*cos (1)*sin(1)
- --------- + ---------- + ----------------- + ---------------- + -----------------
64 64 32 64 64
$$- \frac{7 \sin^{4}{\left(1 \right)}}{64} + \frac{5 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{32} + \frac{25 \cos^{4}{\left(1 \right)}}{64} + \frac{9 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{64} + \frac{23 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{64}$$
-7*sin(1)^4/64 + 25*cos(1)^4/64 + 5*cos(1)^2*sin(1)^2/32 + 9*sin(1)^3*cos(1)/64 + 23*cos(1)^3*sin(1)/64
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.