y
2
y > 2
A 엘
(y – 2)1/3 + 1, 2 <Y<10
Consider a curve r =
19-y
y< 10
The area enclosed by the above curve, tangent to it at x = 2 and X-axis is (in sq. units)
Answers
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0
Answer:
Step-by-step explanation:
Given, equation of the parabola is
(y−2)
2
=(x−1)
or y
2
−4y−x+5=0
The equation of tangent at (2,3) is
3y−2(y+2)−
2
(x+2)
+5=0
⇒2y−x−4=0
∴ Required area A is given by
A=∫
0
3
(x
2
−x
1
)dx
⇒A=∫
0
3
[{(y−2)
2
+1}−{2y−4}]dy
⇒A=∫
0
3
(y
2
−6y+9)dy
=∫
0
3
(3−y)
2
dy=−[
3
(3−y)
3
]
0
3
=9.
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