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If f(x)={{:(x+3 : x lt 3),(3x^(2)+1:xge3...

If `f(x)={{:(x+3 : x lt 3),(3x^(2)+1:xge3):}`, then find `int_(2)^(5) f(x) dx`.

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`underset(2)overset(5)intf(x)dx=underset(2)overset(3)intf(x)dx+underset(5)overset(3)intf(x)dx=underset(2)overset(3)int(x+3)dx+overset(5)underset(3)int(3x^(2)+1)dx=[(x^(2))/(2)+3x]_(2)^(3)+[x^(3)+x]_(3)^(5)`
`= (9-4)/(2)+3(3-2)+5^(3)-3^(3)+5-3=(211)/(2)`
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