MatemáticasAvanzado1 respuestas

Por favor me pordrian ayudar con esto :Evaluar las 2 siguientes integrales impropias si convergen o divergen ?

Por favor me pordrian ayudar con esto : Evaluar las 2 siguientes integrales impropias si convergen o divergen :

En resumen

1) <img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Cint%5Climits_%7B%5Csqrt%7B3%7D%7D%5E%7B%2B%5Cinfty%7D%5Cdfrac%7B3%7D%7Bx%5E2%2B9%7Ddx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cleft.

Mejor respuesta

10

1)

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Cint%5Climits_%7B%5Csqrt%7B3%7D%7D%5E%7B%2B%5Cinfty%7D%5Cdfrac%7B3%7D%7Bx%5E2%2B9%7Ddx%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cleft.%5Carctan%5Cleft%28%5Cdfrac%7Bx%7D%7B3%7D%5Cright%29%5Cright%7C_%7B%5Csqrt%7B3%7D%7D%5E%7B%2B%5Cinfty%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Clim%5Climits_%7Bx%5Cto%2B%5Cinfty%7D%5Carctan%5Cleft%28%5Cdfrac%7Bx%7D%7B3%7D%5Cright%29-%5Carctan%5Cleft%28%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B3%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BNote%20que%20la%20FUNCI%5C%27ON%20%7D%5Carctan%5Ctexttt%7B%20tiene%20como%20imagen%20%7D%5Cleft%28-%5Cdfrac%7B%5Cpi%7D%7B2%7D%2C%5Cdfrac%7B%5Cpi%7D%7B2%7D%5Cright%29%5C%5C%5Ctexttt%7Bpor%20ende%3A%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cdfrac%7B%5Cpi%7D%7B2%7D-%5Cdfrac%7B%5Cpi%7D%7B6%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7BI%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D%7D" />

2)

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D%5Cint%5Climits_%7B-%5Cinfty%7D%5E%7B%2B%5Cinfty%7D%5Cdfrac%7Bdx%7D%7Bx%5E2%2B2x%2B1%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cint%5Climits_%7B-%5Cinfty%7D%5E%7B%2B%5Cinfty%7D%5Cdfrac%7Bdx%7D%7B%28x%2B1%29%5E2%2B1%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cleft.%5Carctan%28x%2B1%29%5Cright%7C_%7B-%5Cinfty%7D%5E%7B%2B%5Cinfty%7D%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Clim%5Climits_%7Bx%5Cto%2B%5Cinfty%7D%5Carctan%20x-%5Clim%5Climits_%7Bx%5Cto-%5Cinfty%7D%5Carctan%20x%5C%5C%20%5C%5C%20%5C%5C%0AI%3D%5Cdfrac%7B%5Cpi%7D%7B2%7D-%5Cleft%28-%5Cdfrac%7B%5Cpi%7D%7B2%7D%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7BI%3D%5Cpi%7D" />.