Question

Determine the area under the curve y = ex between x = (-)2 and x = 3.

a. 19.95 unit^2
b. 19.90 unit^2
c. 19.75 unit^2
d. 11.95 unit^2

Answer 1

The curve $y = e^x$ between $x = (-)2$ and $x = 3$ can be found by the calculation of the integral of this function:

$$f(x) = e^x$$

Let $F(x) = \int f(x) \implies F(x) = \int e^x dx$

if $x = -2$ and $x = 3$, then

$$\int_{-2}^{3} e^x dx = \frac{e^{x} - 1}{e^2} \approx 19.9502$$

Answer: a. 19.95