Question

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

• A. 3
• B. 3 ln (3) - 2
• C. 3 ln (3) + 2
• D. 2

Answer 1

Answer: (D)

2

Answer 2

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) $\Rightarrow \frac{x}{3} = 1 , \Rightarrow x = 3$ Required area $=\int\limits^{3}_{0} \text{ln}\left(3\right) dx - \int\limits^{3}_{1} \text{ln}\left(x\right)dx$ $= \left[x \,\text{ln} \left(3\right)\right]^{3}_{0} - \left[x \,\text{ln} \left(x\right) - x\right]^{3}_{1} = 2$