1. Tardigrade
  2. Question
  3. Mathematics
  4. The area bounded by the curve y = ln (x) and the lines y = 0, y = ln (3) and x = 0 is equal to :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The area bounded by the curve y = ln (x) and the lines y = 0, y = ln (3) and x = 0 is equal to :

Application of Integrals

Solution:

To find the point of intersection of curves y = ln (x)
and y = ln (3), put ln (x) = ln (3)
$\Rightarrow $ ln (x) - ln (3) = 0
$\Rightarrow $ ln (x) - ln (3) = ln (1)
$\Rightarrow \frac{x}{3} = 1 , \Rightarrow x = 3$
image
Required area $ =\int\limits^{3}_{0} \text{ln}\left(3\right) dx - \int\limits^{3}_{1} \text{ln}\left(x\right)dx$
$ = \left[x \,\text{ln} \left(3\right)\right]^{3}_{0} - \left[x \,\text{ln} \left(x\right) - x\right]^{3}_{1} = 2 $