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Quesito 1 |
Calcola il seguente integrale definito
la primitiva di x sin x si calcola per parti ponendo f=x e g'=sin x. In questo modo si ottiene
![[Graphics:Images/index_gr_2.gif]](Images/index_gr_2.gif)
Ora calcoliamo F(π/2)-F(0)
![[Graphics:Images/index_gr_3.gif]](Images/index_gr_3.gif){kind=small}
![[Graphics:Images/index_gr_4.gif]](Images/index_gr_4.gif)
pertanto l'integrale definito sarà pari a 1
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Quesito numero 2 |
Dopo aver disegnato il grafico di ![[Graphics:Images/index_gr_7.gif]](Images/index_gr_7.gif){kind=small}
calcolare ![[Graphics:Images/index_gr_8.gif]](Images/index_gr_8.gif)
e![[Graphics:Images/index_gr_9.gif]](Images/index_gr_9.gif)
Il grafico di 2 exp(-x)-1 è
![[Graphics:Images/index_gr_10.gif]](Images/index_gr_10.gif)
la primitiva della esponenziale vale ∫(2![[Graphics:Images/index_gr_11.gif]](Images/index_gr_11.gif){kind=small}
dx = -2![[Graphics:Images/index_gr_12.gif]](Images/index_gr_12.gif){kind=small}
. Pertanto
![[Graphics:Images/index_gr_5.gif]](Images/index_gr_5.gif){kind=small}
![[Graphics:Images/index_gr_6.gif]](Images/index_gr_6.gif){kind=small}
![[Graphics:Images/index_gr_13.gif]](Images/index_gr_13.gif)
e
![[Graphics:Images/index_gr_14.gif]](Images/index_gr_14.gif){kind=small}
![[Graphics:Images/index_gr_15.gif]](Images/index_gr_15.gif)
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Quesito numero 3 |
Determina il valore di A affiche sia nullo l'integrale![[Graphics:Images/index_gr_17.gif]](Images/index_gr_17.gif)
![[Graphics:Images/index_gr_16.gif]](Images/index_gr_16.gif)
![[Graphics:Images/index_gr_18.gif]](Images/index_gr_18.gif)
Ponendo ora il risultato trovato pari a 0 si ottiene
![[Graphics:Images/index_gr_19.gif]](Images/index_gr_19.gif)
![[Graphics:Images/index_gr_20.gif]](Images/index_gr_20.gif)
![[Graphics:Images/index_gr_21.gif]](Images/index_gr_21.gif)
Infatti dal grafico di (x-1)(x-2)
![[Graphics:Images/index_gr_23.gif]](Images/index_gr_23.gif)
![[Graphics:Images/index_gr_22.gif]](Images/index_gr_22.gif)