Question

how to find the area enclosed by the curve and the x-axis for a function

Answer 1

Find where the function intersects the x-axis.
Integrate over these regions. Be careful because if you integrate over the areas under the x-axis the area will be negative and cancel out positive area. For example, if you integrate sin(x) from 0 to 2pi you will get 0 when in fact you should integrate from 0 to pi and from pi to 2pi since that's where the graph breaks.