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प्रश्न
Evaluate: `int_(-1)^2 |x^3 - 3x^2 + 2x|dx`
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उत्तर
The given definite integral = `int_(-1)^2|x(x - 1)(x - 2)|dx`
= `int_(-1)^0 |x(x - 1)(x - 2)|dx + int_0^1 |x(x - 1)(x - 2)|dx + int_1^2 |x(x - 1)(x - 2)|dx`
= `- int_(-1)^0 (x^3 - 3x^2 + 2x)dx + int_0^1 (x^3 - 3x^2 + 2x)dx - int_1^2 (x^3 - 3x^2 + 2x)dx`
= `- [x^4/4 - x^3 + x^2]_(-1)^0 + [x^4/4 - x^3 + x^2]_0^1 - [x^4/4 - x^3 + x^2]_1^2`
= `9/4 + 1/4 + 1/4 = 11/4`
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