Respuesta :

Since [tex]f'[/tex] is continuous, we have by the fundamental theorem of calculus

[tex]\displaystyle\int_3^7f'(t)\,\mathrm dt=f(7)-f(3)=20[/tex]

We're given that [tex]f(3)=11[/tex], so it follows that [tex]f(7)=31[/tex].