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Question:

The area (in sq. units) of the region bounded by the curves y=2x and y=|x+1|, in the first quadrant is:

32−1;loge2

12

32

loge2+32

Solution:

Required Area = ∫₀¹((x+1)−2x)dx = (x²/2 + x − 2xln2)₀¹ = (1/2 + 1 − 2ln2) − (0 + 0 − 1ln2) = 3/2 − 1ln2