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