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Evaluate int(1)^(4)f(x)dx, where f(x)={{...

Evaluate `int_(1)^(4)f(x)dx`, where `f(x)={{:(4x+3,"if" 1 le x le 2),(3x+5,"if" 2 le x le 4.):}`

Text Solution

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`int_(1)^(4)f(x)dx=int_(1)^(2)f(x)dx+int_(2)^(4)f(x)dx`
`=int_(1)^(2)(4x+3)dx+int_(2)^(4)(3x+5)dx`
`=[2x^(2)+3x]_(1)^(2)+[(3x^(2))/(2)+5x]_(2)^(4)=(9+28)=37`.
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