Sr Examen
Integral de x^(1/2)*cos^2(x^(3/2)) dx
Solución
Ha introducido
[src]
3/2 pi / | | ___ 2/ 3/2\ | \/ x *cos \x / dx | / 0
$$\int\limits_{0}^{\pi^{\frac{3}{2}}} \sqrt{x} \cos^{2}{\left(x^{\frac{3}{2}} \right)}\, dx$$
Integral(sqrt(x)*cos(x^(3/2))^2, (x, 0, pi^(3/2)))
Respuesta (Indefinida)
[src]
/ | 3/2 2/ 3/2\ 3/2 2/ 3/2\ / 3/2\ / 3/2\ | ___ 2/ 3/2\ x *cos \x / x *sin \x / cos\x /*sin\x / | \/ x *cos \x / dx = C + --------------- + --------------- + ------------------- | 3 3 3 /
$$\int \sqrt{x} \cos^{2}{\left(x^{\frac{3}{2}} \right)}\, dx = C + \frac{x^{\frac{3}{2}} \sin^{2}{\left(x^{\frac{3}{2}} \right)}}{3} + \frac{x^{\frac{3}{2}} \cos^{2}{\left(x^{\frac{3}{2}} \right)}}{3} + \frac{\sin{\left(x^{\frac{3}{2}} \right)} \cos{\left(x^{\frac{3}{2}} \right)}}{3}$$
Gráfica
Respuesta
[src]
/ 9/4\ / 9/4 \ / 9/4\ / 9/4\ / 9/4 \ / 9/4\ / 9/4 \
3|pi | |pi | |pi | 4|pi | |pi | 2|pi | |pi |
2*tan |-----| 2*|----- - pi| 2*tan|-----| 2*tan |-----|*|----- - pi| 4*tan |-----|*|----- - pi|
2*pi \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 /
---- - --------------------------------- + --------------------------------- + --------------------------------- + --------------------------------- + ---------------------------------
3 / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\
4|pi | 2|pi | 4|pi | 2|pi | 4|pi | 2|pi | 4|pi | 2|pi | 4|pi | 2|pi |
3 + 3*tan |-----| + 6*tan |-----| 3 + 3*tan |-----| + 6*tan |-----| 3 + 3*tan |-----| + 6*tan |-----| 3 + 3*tan |-----| + 6*tan |-----| 3 + 3*tan |-----| + 6*tan |-----|
\ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 /
$$- \frac{2 \tan^{3}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right) \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \tan{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{4 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right) \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right)}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \pi}{3}$$
=
=
/ 9/4\ / 9/4 \ / 9/4\ / 9/4\ / 9/4 \ / 9/4\ / 9/4 \
3|pi | |pi | |pi | 4|pi | |pi | 2|pi | |pi |
2*tan |-----| 2*|----- - pi| 2*tan|-----| 2*tan |-----|*|----- - pi| 4*tan |-----|*|----- - pi|
2*pi \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 /
---- - --------------------------------- + --------------------------------- + --------------------------------- + --------------------------------- + ---------------------------------
3 / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\ / 9/4\
4|pi | 2|pi | 4|pi | 2|pi | 4|pi | 2|pi | 4|pi | 2|pi | 4|pi | 2|pi |
3 + 3*tan |-----| + 6*tan |-----| 3 + 3*tan |-----| + 6*tan |-----| 3 + 3*tan |-----| + 6*tan |-----| 3 + 3*tan |-----| + 6*tan |-----| 3 + 3*tan |-----| + 6*tan |-----|
\ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 /
$$- \frac{2 \tan^{3}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right) \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \tan{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{4 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right) \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)}}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \left(- \pi + \frac{\pi^{\frac{9}{4}}}{2}\right)}{3 \tan^{4}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 6 \tan^{2}{\left(\frac{\pi^{\frac{9}{4}}}{2} \right)} + 3} + \frac{2 \pi}{3}$$
2*pi/3 - 2*tan(pi^(9/4)/2)^3/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2) + 2*(pi^(9/4)/2 - pi)/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2) + 2*tan(pi^(9/4)/2)/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2) + 2*tan(pi^(9/4)/2)^4*(pi^(9/4)/2 - pi)/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2) + 4*tan(pi^(9/4)/2)^2*(pi^(9/4)/2 - pi)/(3 + 3*tan(pi^(9/4)/2)^4 + 6*tan(pi^(9/4)/2)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.