Question

use the definite integral to find the area between the x axis and f(x) over the indicated interval.

f(x)= 3e^x -4; [-3,4]

the area between the x asix and f(x) is ?

Answer 1

Step 1:

The function is .

Find the area between function and -axis on the interval .

The area of the region bounded by the graphs of and and the vertical lines and is .

Consider -axis as .

Graph:

Graph the functions and on the interval .

Observe the graph:

The intersection point of two functions is .

on the interval .

on the interval .

Step 2:

The area of the region is .

Substitute and .

.

Area between the -axis and is .

Solution:

Area between the -axis and is .