JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(12 \int \limits_0^3\left|x^2-3 x+2\right| d x\) is \(.............\)
- A \(20\)
- B \(25\)
- C \(22\)
- D \(65\)
Answer & Solution
Correct Answer
(C) \(22\)
Step-by-step Solution
Detailed explanation
\(12 \int \limits_0^3\left| x ^2-3 x +2\right| dx\) \(={ }_{12} \int_0^3\left|\left( x -\frac{3}{2}\right)^2-\frac{1}{4}\right| dx\) If \(x-\frac{3}{2}=t\) \(dx = dt\) \(=24 \int \limits_0^{3 / 2}\left| t ^2-\frac{1}{4}\right| dt\)…
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