The area bounded by the curves y=|x2-1| and y=1 is

Question

The area bounded by the curves y=|x2-1| and y=1 is (A) (2/3)(√2+1) (B) (4/3)(√2-1) (C) 2(√2-1) (D) (8/3)(√2-1)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f755138cddf860a0ec95ff3dcb4a24c9-.png" /> Area = text ABCDEA =2(∫ limits01(1-(1-x2)) d x+∫ limits1√2(1-(x2-1)) d x) =(8/3)(√2-1)

Q. The area bounded by the curves $y = ∣ ∣ x^{2} - 1 ∣ ∣$ and $y = 1$ is

$\frac{2}{3} (2 + 1)$

$\frac{4}{3} (2 - 1)$

$2 (2 - 1)$

$\frac{8}{3} (2 - 1)$

Area $= ABCDEA$
$= 2 (0 \int 1 (1 - (1 - x^{2})) d x + 1 \int 2 (1 - (x^{2} - 1)) d x)$
$= \frac{8}{3} (2 - 1)$

Q. The area bounded by the curves y=∣∣​x2−1∣∣​ and y=1 is

32​(2​+1)

34​(2​−1)

2(2​−1)

38​(2​−1)