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Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
If $\int_1^k(2 x-3) d x=12$, then $k$ =
  • ✓
    -2 and 5
  • B
    5
  • C
    2
  • D
    -5
✓

Answer

Correct option: A.
-2 and 5
(A)
$\int_1^k(2 x-3) d x=12$
$\Rightarrow\left[x^2-3 x\right]_1^{ k }=12 \\ \Rightarrow\left( k ^2-3 k \right)-(1-3)=12 \\ \Rightarrow k ^2-3 k -10=0 \\ \Rightarrow( k -5)( k +2)=0 \\ \Rightarrow k =-2,5$

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