The area bounded by the curve y = x between the x-axis and ordina… - Vidyadip

MCQ

The area bounded by the curve $y = \log x$ between the $x$-axis and ordinate $x = e$ is

A
$e$
✓
$1$
C
$\infty $
D
None of these

✓

Answer

Correct option: B.

$1$

b
(b) We have, $y = \log x$.....$(i)$
and ordinate $x = e$
Now substitute $y = 0$ in equation $(i),$ we get $0 = \log x$ or $x = 1$.
$\therefore$ Area bounded by the curve between $x = 1$ and $x = e$ is, $A = \int_{{x_1}}^{{x_2}} {ydx} = \int_1^e {\log x\,dx} $
$A = [x\log x]_1^e - \int_1^e {\frac{1}{x}.x\,dx = e - e + 1 = 1} $.

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