Solve...
x^2 - xy -2y^2 +2x +3
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Answers
Answered by
1
Answer:
The equation of the curve is x
2
+2x+y−3=0
or x
2
+2x+1+y−3−1=0 (add and subtract 1)
⇒y−4=−(x+1)
2
The curve meets the y−axis at (0,3) and the x−axis at (−3,0) and (1,0)
The tangent at (0,3) is y−3=−2(x−0)
The required area=area of △OAB−the shaded area(OCB)
=
2
1
.
2
3
.3−∫
0
1
(4−(x+1)
2
)dx
=
4
9
−[4x−
3
(x+1)
3
]
0
1
=
4
9
−[(4−
3
8
)+
3
1
]
=
4
9
−4+
3
7
=
12
7
.sq.unit
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