Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$3 a \int_0^1\left(\frac{a x-1}{a-1}\right)^2 d x=$
✓
$a-1+(a-1)^{-2}$
B
$a+a^{-2}$
C
$a-a^{-2}$
D
$a^2+\frac{1}{a^2}$
✓
Answer
Correct option: A.
$a-1+(a-1)^{-2}$
(A) $3 a \int_0^1\left(\frac{ a x-1}{ a -1}\right)^2 d x=\frac{3 a }{( a -1)^2} \int_0^1( a x-1)^2 d x$ $=\frac{3 a \left[( ax -1)^3\right]_0^1}{3 a ( a -1)^2}$ $=\frac{1}{(a-1)^2}\left[(a-1)^3+1\right]$ $=(a-1)+(a-1)^{-2}$
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