Find the area of the region bounded by the graphs of the equations:
y=x2,y=−x+6,y=0
Final Answer
S=1032
Solution
First, we find out how the area looks like:
x2=−x+6
x2+x−6=0
(x−2)(x+3)=0
x=2,x=−3
The area looks like this:
Hence, it is a sum of two disjoint areas:
We will calculate them seperately:
S=S1+S2
The first area:
S1=∫02x2dx=
=[3x3]02=
=323−303=
=38
The second area:
S2=∫26−x+6dx=
=[−2x2+6x]26=
=−262+6⋅6−(−222+6⋅2)=
=−236+36−(−2+12)=
=18−10=
=8
Hence, we got
S2=8
Lastly, we sum up the results:
S=S1+S2=
=38+8=
=1032
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