Question

The area bounded by the curve y = ln(x) and the line y = 0, y = ln(3) and x = 0 is equal to

Answer 1

Answer:

Step-by-step explanation:

Hi,

Given curve is y = ln(x) ,

Need to find the area bounded by the curve y = ln(x)  and the line y = 0 ,

y = ln(3) and x = 0.

Area bounded by the x-axis and the curve y = f(x) between the limits x= b and

x = a is given by

$\int\limits^a_b {f(x)} \, dx$.

Thus, the required area will be Area of rectangle OBPN - Area under the

curve AP bounded between x =1 and x = 3

3ln(3) - $\int\limits^3_1 {ln(x)} \, dx$

=3ln(3) - [xln(x) - x]₁³

=3ln(3) - [3ln(3) - 3 +1]

= 2 sq. units

Hope, it helped !