Question

 The area of the region bounded by the curve y = 1/x , the x-axis and between x = 1 to x = 6 is: 


(a) log 4 sq. units

(b) log 6 sq. units

(c) log 8 sq. units

(d) none of these​

Answer 1

Answer:

(1+x)

dx

dy

−xy=1−x

dx

dy

+(

1+x

−x

)y=

1+x

1−x

∫pdx=∫

1+x

−x

=−∫

1+x

1+x−1

dx

=−∫1−

1+x

1

dx

=−x+log∣1+x∣dx

I.Fe

∫pdx

=e

log(1+x)−x

=

e

x

1+x

4.5y.

e

x

1+x

=∫

e

x

1−x

y

e

x

(1+x)

=∫e

−x

(1−x)

y(1+x)=e

x

c

−x

(+x)

y(1+x)=x

Answer 2

Answer:

(B)The area of the region bounded by the curve is $(log_{e}6)sq.units$

Step-by-step explanation:

Given that,

The curve  $y=\frac{1}{x}$ bounds a region between the abscissa x=1 and x=6.

We are required to find the area enclosed between the curve and x-axis in between the given lines.

To solve this problem,we shall use definite integration in between the given limits.The area enclosed by the curve is $A=\int\limits^a_b {y} \, dx$

Substituting the given limits and curve in above relation,we get-

$A=\int\limits^6_1 {\frac{1}{x} } \, dx =(log_{e})\limits^6_1=log_{e}6-log_{e}1\\=log_{e}\frac{6}{1} =log_{e}6$

Therefore,the area of the region bounded by the curve is found to be $(log_{e}6)sq.units$

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