Application of Integrals: The area (in sq. units) of the region bounded by the curves y=2^x… | JEE Main 2019

JEE Main 2019 (Online) 10th April Evening ShiftQuestion 1

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

Application of Integrals

$\frac32-\frac{1}{\log_e2}$✓ Correct answer$\frac12$$\log_e2+\frac32$$\frac32$

Solution

Curves meet at $x=0,1$ with $x+1\ge2^x$ between. Area $=\int_0^1(x+1-2^x)dx=\frac32-\frac1{\ln2}$.

Application of Integrals - JEE Mathematics question (JEE Main 2019 (Online) 10th April Evening Shift)