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The area bounded by the axes of referenc...

The area bounded by the axes of reference and the normal to `y=log_(e)x` at (1,0), is

A

1 sq. unit

B

2 sq. units

C

`(1)/(2)` sq. unit

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`y=log_(e)x rArr (dy)/(dx) = (1)/(x) rArr ((dy)/(dx)) _(p) = 1`
The equation of the normal at (1, 0) is
`y-0= -1 (x-1) rArr x+y=1`
Clearly, it makes a triangle of area `(1)/(2)` sq. unit with the coordinate axes.
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OBJECTIVE RD SHARMA ENGLISH-TANGENTS AND NORMALS-Chapter Test
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  2. The abscissa of the point on the curve ay^(2)=x^(3), the normal at whi...

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  3. If the curves (x^2)/(a^2)+(y^2)/(b^2)=1 and (x^2)/(l^2)-(y^2)/(m^2)=1c...

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  4. The length of normal at any point to the curve, y=c cosh(x/c) is

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  11. The curve y-e^(xy)+x=0 has a vertical tangent at the point:

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  12. The tangent to the curve given by x = e^(t) cos t y = e^(t) " sin t ...

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  13. The length of the normal at t on the curve x=a(t+sint), y=a(1-cos t), ...

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