Area Under the Curve
Area Under a Curve
JEE Main 2017
Grade 12
Question:
The area bounded by the curve $y = \ln x$, the $x$-axis, and the lines $x = 1$ and $x = e$ is:
(1) $1$
(2) $e - 1$
(3) $e$
(4) $e - 2$
Step-by-Step Solution
Key Concept: Recognise the (geometric) area as $\int_1^e \ln x \, dx$ and apply integration by parts with $u = \ln x$, $dv = dx$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)