Question:
\(\int_0^2 |2x^2-9x+9|dx=\)
\(\int_0^2 |2x^2-9x+9|dx=\)
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Always find sign-change points inside interval for modulus integrals.
Updated On: Jun 22, 2026
- \(\frac{27}{4}\)
- \(\frac{171}{4}\)
- 16
- \(\frac{71}{12}\) \bigskip
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The Correct Option is D
Solution and Explanation
Concept:
Find roots of quadratic to split modulus.
Step 1: Find roots.
\[ 2x^2-9x+9=0 \Rightarrow x=\frac{3}{2},3 \] Only \(1.5\) lies in [0,2].
Step 2: Split integral.
Evaluate sign change at \(x=\frac{3}{2}\)
Step 3: Compute.
\[ \int_0^2 |f(x)|dx=\frac{71}{12} \] \[ \boxed{(D)} \]
Step 1: Find roots.
\[ 2x^2-9x+9=0 \Rightarrow x=\frac{3}{2},3 \] Only \(1.5\) lies in [0,2].
Step 2: Split integral.
Evaluate sign change at \(x=\frac{3}{2}\)
Step 3: Compute.
\[ \int_0^2 |f(x)|dx=\frac{71}{12} \] \[ \boxed{(D)} \]
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