Evaluate: `(i) \int_(-1)^1f(x)dx ,\where\, f(x)={1-2x ,xlt=0 ;1+2x ,xgt=0} ,` ` (ii)\ int_(-1)^4f(x)dx ,\where\, f(x)={2x+8,-1lt=xlt=2; 6x, 2lt=xlt=4}`

Explanation

`(i)int_(-1)^1f(x)dx `

`=int_(-1)^0f(x)dx+int_(1)^2f(x)dx`

`=int_(-1)^0(1-2x)dx+int_(1)^2(2x+1)dx`

`= (x-(2x^2)/2)_(-1)^0 +((2x^2)/2+x)_1^2)`

`= (x-x^2)_(-1)^0 +(x^2+x)_1^2)`

`=[(0−0)−(−1−1)+[1+1−0]`

`=[2]+[2−0]=4`


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