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Q.

The value of ∫dx4x−3−x2 is equal to

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a

sin−1⁡(x−1)+C

b

log⁡(x−2)+4x−3−x2

c

log⁡(x−1)+4x−3−x2+C

d

sin−1⁡(x−2)+C

answer is D.

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Detailed Solution

4x−3−x2=−x2−4x+3=−(x−2)2−1=1−(x−2)2So, ∫dx4x−3−x2=∫dx1−(x−2)2=sin−1⁡(x−2)+C
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