Evaluate the following integrals: `int_0^9f(x)dx ,w h e r ef(x)=`
`{sinx,0 lt=xlt=pi//2`
`1,pi/2lt=xlt=3`
`e^(x-3),3lt=xlt=9`

Explanation

We have,` int_{0}^{9} f(x) d x`
`

=int_{0}^{frac{pi}{2}} sin x d x+int_{frac{pi}{2}}^{3} 1 d x+int_{3}^{9} e^{x-3} d x `
`
=[-cos x]_{0}^{frac{pi}{2}}+[x]_{frac{pi}{2}}^{3}+[e^{x-3}]_{3}^{9} `
`
=[-cos frac{pi}{2}+cos 0]+[3-frac{pi}{2}] `
`
+[e^{9-3}-e^{3-3}] `
`
=[0+1]+[3-frac{pi}{2}]+[e^{6}-e^{0}] `
`
=1+3-frac{pi}{2}+e^{6}-1`
`
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