The area (in sq. units) of the region x ,   y ∈ R 2 : x 2 ≤ y ≤ 3 - 2 x , is.

The area (in sq. units) of the region x, y∈R2:x2≤y≤3-2x, is.
  1. 323
  2. 343
  3. 293
  4. 313

Solution

Point of intersection of y=x2 & y=-2x+3, is obtained by x2+2x-3=0⟹x=-3,1.

So, area of the required region is

∫-313-2x-x2 dx

=3x-x2-x33-31=323.

Asked in: MHT CET Full Test 8

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