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

Step-by-step solution

We know that x =       x , x ≥ 0 - x , x < 0 Hence, x + 1 =           x + 1 , x ≥ - 1 - x + 1 , x < - 1 The graph of the given functions is The shaded area is the required area. Area = ∫ 0 1 y l i n e - y c u r v e d x Area = ∫ 0 1 x + 1 - 2 x d x Using ∫ x n d x = x n + 1 n + 1   &   ∫ a x d x = a x log e a , we get Area = x 2 2 + x - 2 x log e 2 0 1 Area = 1 2 + 1 - 2 log e 2 -   0 + 0 - 1 log e 2 Area = 3 2 - 1