The area (in sq. units) bounded by the curve |.y|.=|ln |x|| and the coordinate axes is

Question

The area (in sq. units) bounded by the curve |.y|.=|ln |x|| and the coordinate axes is (A) 2 (B) 4 (C) 6 (D) 8

Tardigrade Admin · Accepted Answer

Curve |y|=|ln |x|| is <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-wdxis4fxhavkp17o.jpg" /> Required Area =4× |.∫ limits01 (. ln x .)|.dx =4× |x ln x - x|01 =4(|- 1|)=4 sq. units

Q. The area (in sq. units) bounded by the curve $∣ y ∣ = ∣ l n ∣ x ∣ ∣$ and the coordinate axes is

$2$

$4$

$6$

$8$

Curve $∣ y ∣ = ∣ l n ∣ x ∣ ∣$ is

Required Area $= 4 \times ∣ 0 \int 1 (l n x) ∣ d x$
$= 4 \times ∣ x l n x - x ∣_{0}^{1}$
$= 4 (∣ - 1 ∣) = 4$ sq. units

Q. The area (in sq. units) bounded by the curve ∣y∣=∣ln∣x∣∣ and the coordinate axes is

2

4

6

8

Curve ∣y∣=∣ln∣x∣∣ is Required Area =4×∣0∫1​(lnx)∣dx =4×∣xlnx−x∣01​ =4(∣−1∣)=4 sq. units

Q. The area (in sq. units) bounded by the curve $∣ y ∣ = ∣ l n ∣ x ∣ ∣$ and the coordinate axes is

$2$

$4$

$6$

$8$

Curve $∣ y ∣ = ∣ l n ∣ x ∣ ∣$ is

Required Area $= 4 \times ∣ 0 \int 1 (l n x) ∣ d x$
$= 4 \times ∣ x l n x - x ∣_{0}^{1}$
$= 4 (∣ - 1 ∣) = 4$ sq. units