a) Calcular 
b) Calcular 
Solución:
a) Las indeterminaciones del tipo 0/0 las resolvemos utilizando la regla de L’Hôpital:
b) Se trata de una integral inmediata:
![\displaystyle\int_0^{\pi/2}(\text{sen}(x)+\cos(x))~dx=\Big[-\cos(x)+\text{sen}(x)\Big]_0^{\pi/2}=\\\\=\left(-\cos\left(\frac\pi2\right)+\text{sen}\left(\frac\pi2\right)\right)-\Big(-\cos(0)+\text{sen}(0)\Big)=\\\\=(0+1)-(-1+0)=\boxed2](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%5Cint_0%5E%7B%5Cpi%2F2%7D%28%5Ctext%7Bsen%7D%28x%29%2B%5Ccos%28x%29%29%7Edx%3D%5CBig%5B-%5Ccos%28x%29%2B%5Ctext%7Bsen%7D%28x%29%5CBig%5D_0%5E%7B%5Cpi%2F2%7D%3D%5C%5C%5C%5C%3D%5Cleft%28-%5Ccos%5Cleft%28%5Cfrac%5Cpi2%5Cright%29%2B%5Ctext%7Bsen%7D%5Cleft%28%5Cfrac%5Cpi2%5Cright%29%5Cright%29-%5CBig%28-%5Ccos%280%29%2B%5Ctext%7Bsen%7D%280%29%5CBig%29%3D%5C%5C%5C%5C%3D%280%2B1%29-%28-1%2B0%29%3D%5Cboxed2&bg=ffffff&fg=141412&s=0&c=20201002 "\displaystyle\int_0^{\pi/2}(\text{sen}(x)+\cos(x))~dx=\Big[-\cos(x)+\text{sen}(x)\Big]_0^{\pi/2}=\\\\=\left(-\cos\left(\frac\pi2\right)+\text{sen}\left(\frac\pi2\right)\right)-\Big(-\cos(0)+\text{sen}(0)\Big)=\\\\=(0+1)-(-1+0)=\boxed2")
♦
a) Calcular
b) Calcular
Solución:
a) Las indeterminaciones del tipo 0/0 las resolvemos utilizando la regla de L’Hôpital:
b) Se trata de una integral inmediata:
♦