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we have to evaluate ,
here we have considered modulus function
so first of all, we have to break modulus function.
let f(x) = |x² + 2x - 3|
for 0 < x < 1 , x² + 2x - 3 < 0
so, f(x) = -(x² + 2x - 3) , for 0 < x < 1
for 1 < x < 2, x² + 2x - 3 > 0
so, f(x) = x² + 2x - 3, for 1 < x < 2
now applying application,
then, integration converts into
=
= -[1/3 +1 - 3 - (0 + 0 - 0) ] + [(2)³/3 + (2)² - 3(2) - {(1)³/3 + (1)² - 3 }]
= -[ 4/3 - 3 ] + [8/3 + 4 - 6 - 4/3 + 3]
= -4/3 + 3 + [4/3 + 1 ]
= 4 [ Ans]
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