Question

. Find the area of the region bounded by the curve y = 1 [1] x axis and between x = 1, x = 4.

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Answer 1

Answer:

ln (3) square units.

Step-by-step explanation:

Here, the given function is y = \frac{1}{x}y=

x

1

and we have to calculate the area between the ordinates x = 2 to x = 6.

So, A = \int\limits^6_2 {\frac{1}{x} } \, dx

2

∫

6

x

1

dx

{It is the area bounded by the curve itself at the top, x-axis at the bottom and the ordinates x = 2 and x = 6 at the two sides.}

⇒ A = [\ln x]_{2} ^{6} = \ln 6 - \ln 2 = \ln \frac{6}{2} = \ln 3[lnx]

2

6

=ln6−ln2=ln

2

6

=ln3 square units. (Answer)

{Since, we know the logarithmic property ln A - ln B = ln A/B}

Explanation:

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