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Q.

Slope of normal to a curve y=f(x) at any point on curve is xy and curve is passing  through the point (1,1) . Then area formed by y=f(x),x - axis x=3 and x=5 is

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a

53

b

log53

c

log15

d

1

answer is B.

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Detailed Solution

−dxdy=xy⇒ydx+xdy=0d(xy)=0xy=c(1,1)⇒xy=1 Area =∫35 1xdx=[log⁡x]35=log⁡5−log⁡3=log⁡(5/3)
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