Area bounded by the curve y= log x and the coordinate axes is

Question

Area bounded by the curve y= log x and the coordinate axes is (A) 2 (B) 1 (C) 5 (D) 2 √2

Tardigrade Admin · Accepted Answer

Observing the graph of log x, we find that the required area lies below x -axis between x=0 and x=1. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/7c89fe31ed055dcf09c0d5725d6776fb-.png" /> So required area =|∫ limits01 log x d x | =|(x log x-x)|01=|-1|=1

Q. Area bounded by the curve $y = lo g x$ and the coordinate axes is

$2$

$1$

$5$

$22$

Observing the graph of $lo g x$ , we find that the required area lies below $x$ -axis between $x = 0$ and $x = 1$ .

So required area $= ∣ ∣ 0 \int 1 lo g x d x ∣ ∣$
$= ∣ (x lo g x - x) ∣_{0}^{1} = ∣ - 1∣ = 1$

Q. Area bounded by the curve y=logx and the coordinate axes is

2

1

5

22​

Observing the graph of logx, we find that the required area lies below x -axis between x=0 and x=1. So required area =∣∣​0∫1​logxdx∣∣​ =∣(xlogx−x)∣01​=∣−1∣=1

Q. Area bounded by the curve $y = lo g x$ and the coordinate axes is

$2$

$1$

$5$

$22$

Observing the graph of $lo g x$ , we find that the required area lies below $x$ -axis between $x = 0$ and $x = 1$ .

So required area $= ∣ ∣ 0 \int 1 lo g x d x ∣ ∣$
$= ∣ (x lo g x - x) ∣_{0}^{1} = ∣ - 1∣ = 1$