Sr Examen
Integral de cos12(2*x) dx
Solución
Ha introducido
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1 / | | 12 | cos (2*x) dx | / 0
$$\int\limits_{0}^{1} \cos^{12}{\left(2 x \right)}\, dx$$
Integral(cos(2*x)^12, (x, 0, 1))
Respuesta (Indefinida)
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/ | 3 3 5 | 12 sin (4*x) sin (8*x) sin(4*x) 3*sin (4*x) 31*sin(8*x) 33*sin(16*x) 231*x | cos (2*x) dx = C - --------- - --------- + -------- + ----------- + ----------- + ------------ + ----- | 24 12288 8 640 1024 16384 1024 /
$$\int \cos^{12}{\left(2 x \right)}\, dx = C + \frac{231 x}{1024} + \frac{3 \sin^{5}{\left(4 x \right)}}{640} - \frac{\sin^{3}{\left(4 x \right)}}{24} + \frac{\sin{\left(4 x \right)}}{8} - \frac{\sin^{3}{\left(8 x \right)}}{12288} + \frac{31 \sin{\left(8 x \right)}}{1024} + \frac{33 \sin{\left(16 x \right)}}{16384}$$
Gráfica
Respuesta
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11 9 7 3 5 231 cos (2)*sin(2) 11*cos (2)*sin(2) 33*cos (2)*sin(2) 77*cos (2)*sin(2) 77*cos (2)*sin(2) 231*cos(2)*sin(2) ---- + --------------- + ----------------- + ----------------- + ----------------- + ----------------- + ----------------- 1024 24 240 640 1024 1280 2048
$$\frac{231 \sin{\left(2 \right)} \cos{\left(2 \right)}}{2048} + \frac{77 \sin{\left(2 \right)} \cos^{3}{\left(2 \right)}}{1024} + \frac{77 \sin{\left(2 \right)} \cos^{5}{\left(2 \right)}}{1280} + \frac{33 \sin{\left(2 \right)} \cos^{7}{\left(2 \right)}}{640} + \frac{11 \sin{\left(2 \right)} \cos^{9}{\left(2 \right)}}{240} + \frac{\sin{\left(2 \right)} \cos^{11}{\left(2 \right)}}{24} + \frac{231}{1024}$$
=
=
11 9 7 3 5 231 cos (2)*sin(2) 11*cos (2)*sin(2) 33*cos (2)*sin(2) 77*cos (2)*sin(2) 77*cos (2)*sin(2) 231*cos(2)*sin(2) ---- + --------------- + ----------------- + ----------------- + ----------------- + ----------------- + ----------------- 1024 24 240 640 1024 1280 2048
$$\frac{231 \sin{\left(2 \right)} \cos{\left(2 \right)}}{2048} + \frac{77 \sin{\left(2 \right)} \cos^{3}{\left(2 \right)}}{1024} + \frac{77 \sin{\left(2 \right)} \cos^{5}{\left(2 \right)}}{1280} + \frac{33 \sin{\left(2 \right)} \cos^{7}{\left(2 \right)}}{640} + \frac{11 \sin{\left(2 \right)} \cos^{9}{\left(2 \right)}}{240} + \frac{\sin{\left(2 \right)} \cos^{11}{\left(2 \right)}}{24} + \frac{231}{1024}$$
231/1024 + cos(2)^11*sin(2)/24 + 11*cos(2)^9*sin(2)/240 + 33*cos(2)^7*sin(2)/640 + 77*cos(2)^3*sin(2)/1024 + 77*cos(2)^5*sin(2)/1280 + 231*cos(2)*sin(2)/2048
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.