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Byju's Answer
Standard XII
Mathematics
Area between x=g(y) and y Axis
The area boun...
Question
The area bounded by the curve y = log
e
x and x-axis and the straight line x = e is
(a) e sq. units
(b) 1 sq. units
(c) 1−
1
e
sq. units
(d) 1+
1
e
sq. units
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Solution
(b) 1 sq. units
The point of intersection of the curve and the straight line is A(e, 1).
Therefore, the area of the required region ABC,
A
=
∫
0
1
x
1
-
x
2
d
y
where
,
x
1
=
e
and
x
2
=
e
y
=
∫
0
1
e
-
e
y
d
y
=
e
y
-
e
y
0
1
=
e
1
-
e
1
-
e
0
-
e
0
=
e
-
e
+
1
=
1
square
unit
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Similar questions
Q.
The area bounded by the curve y = log
e
x and x-axis and the straight line x = e is
(a) e sq. units
(b) 1 sq. units
(c) 1−
1
e
sq. units
(d) 1+
1
e
sq. units