find the area enclosed by line y=x+2 within the limits x=2 and x=5
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It is always a good idea to draw the functions if possible(i.e if you know the graphs of the functions, and you should learn some basic graphs like lines,sin and cos, roots,etc.), then find the intersection points between the two function which are in this case x=5,x=−12x=5,x=−12 as the other answers show. Here is a graph of these functions

and as the graph shows 60−7x60−7x is above x2x2 thus the area is
A===∫5−1260−7x−x2dx60x−7x22−x33∣5−1249136.

and as the graph shows 60−7x60−7x is above x2x2 thus the area is
A===∫5−1260−7x−x2dx60x−7x22−x33∣5−1249136.
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