Exam

JEE Main

Year

2013

Date

9 April

Mode

Online

Subject

Mathematics

Chapter

Area Under Curves

JEE Main 2013 · 9 April · Online · Mathematics · Area Under Curves

The area bounded by the curve y= (x) and the lines y=0, y= (3) and...

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

Step-by-step solution

To find the point of intersection of curves $$\begin{aligned}& y=\ln (x) \text{\text{ and } }y=\ln (3),\text{ put } \ln (x)=\ln (3) \\ \Rightarrow & \ln (x)-\ln (3)=0 \\ \Rightarrow & \ln (x)-\ln (3)=\ln (1) \\ \Rightarrow & \frac{x}{3}=1, \Rightarrow x=3 \end{aligned}$$$\\$$\begin{aligned} \text{ Required area } & =\int_0^3 \ln (3) d x-\int_1^3 \ln (x) d x \\ = & {[x \ln (3)]_0^3-\left[x \ln (x)-x_1^3=2\right.}\end{aligned}$$