Find the area of the region bounded by the graphs of the equations:
y=x2−2x−3,y=−x+3,x=0,x≥0
Final Answer
S=1321
Solution
First, we find out how the area looks like:
x2−2x−3=−x+3
x2−x−6=0
(x+2)(x−3)=0
x=−2,x=3
But the requested area is only for x positive, therefore only the point x = 3 is relevant.
The area looks like this:
S=∫03−x+3−(x2−2x−3)dx=
S=∫03−x2+x+6dx=
=[−3x3+2x2+6x]03=
=−333+232+6⋅3−(−303+202+6⋅0)=
=−9+29+18−0=
=9+29=
=1321
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