Find the area of the region enclosed by curves X^4=1+y, y=4-4X^2?
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Find the area of the region enclosed by the curves y=4x−x
2
,y=5−2x
Medium
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Video Explanation
Solution To Question ID 609399
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Answer
The point of intersection of the parabola and the line is given by
4x−x
2
=5−2x
x
2
−6x+5=0
(x−1)(x−5)=0
Hence x=1 and x=5.
Therefore, the area bounded by the parabola and the line between x=1 and x=5 is given as
A=∫
1
5
(5−2x)−(4x−x
2
)dx
=∫
1
5
x
2
−6x+5dx
=[
3
x
3
−3x
2
+5x]
1
5
=
3
125
−75+25−
3
1
+3−5
=
3
124
−50−2
=
3
124
−52
=
3
124−156
=
3
−32
Hence area is ∣A∣=
3
32
Step-by-step explanation:
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