JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Area Under Curves

The area(in sq. units) of the region bounded by the curves

y = 2^{x}

and

y = ∣ x + 1∣

in the first quadrant is

Answer: (C)

Solution

In the first quadrant

∣ x + 1∣ = x + 1

, so we need the area between

y = x + 1

and

y = 2^{x}

. They cross where

2^{x} = x + 1

, at

x = 0

where both equal

1

and at

x = 1

where both equal

2

, and on

(0, 1)

the line lies above the curve. The area is

\int_{0}^{1} [(x + 1) - 2^{x}] d x = [\frac{x ^{2}}{2} + x - \frac{2 ^{x}}{l n 2}]_{0}^{1} = (\frac{3}{2} - \frac{2}{l n 2}) - (- \frac{1}{l n 2}) = \frac{3}{2} - \frac{1}{l n 2}

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option