Evaluate: `Int_0^3 F(X)Dx` Where F(X) = `{(Cos 2x, 0<= X <= Pi/2),(3, Pi/2 <= X <= 3) :}` - Mathematics

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Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`

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Solution

`int_0^3 f(x) dx = int_0^(pi/2) cos 2x dx + int_(pi/2)^3 dx`

`= (sin 2x/2)_0^(pi/2) + [3x]_(pi/2)^3`

`= [(sin 2 xx  pi/2)/2 - (sin 2 xx 0)/2] + [(3 xx 3 - 3 xx pi/2)]`

`= 0 + 9 - (3pi)/2`

`= 9- (3pi)/2`

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2014-2015 (March)

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