The area (in sq.

Question

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

Accepted Answer

In the first quadrant, $|x+1|=x+1$ for $x\ge0$.

$$\text{Area} = \int_0^1\left[(x+1)-2^x\right]dx = \left[\frac{x^2}{2}+x-\frac{2^x}{\ln2}\right]_0^1$$

$$= \left(\frac12+1-\frac{2}{\ln2}\right) - \left(-\frac{1}{\ln2}\right) = \frac32-\frac{1}{\ln2}$$

Solutions · 1