The area bounded by y -1=| x |, y =0 and | x |=(1/2) will be :

Question

The area bounded by y -1=| x |, y =0 and | x |=(1/2) will be : (A) (3/4) (B) (3/2) (C) (5/4) (D) None of these

Tardigrade Admin · Accepted Answer

The given lines are, y -1= x , x ≥ 0 ; y -1=- x , x <0 y =0 ; x =-(1/2), x <0 ; x =(1/2), x ≥ 0 so that the area bounded is as shown in the figure. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/16424133f458a3c2b90ecd6b0bf42da0-.png" /> Required area =2 ∫ limits01 / 2(1+ x ) dx =2(x+(x2/2))01 / 2=(5/4)

Q. The area bounded by $y - 1 = ∣ x ∣, y = 0$ and $∣ x ∣ = \frac{1}{2}$ will be :

$\frac{3}{4}$

$\frac{3}{2}$

$\frac{5}{4}$

None of these

The given lines are, $y - 1 = x, x \geq 0; y - 1 = - x, x < 0$
$y = 0; x = - \frac{1}{2}, x < 0; x = \frac{1}{2}, x \geq 0$
so that the area bounded is as shown in the figure.

Required area $= 2 0 \int 1/2 (1 + x) d x = 2 (x + \frac{x ^{2}}{2})_{0}^{1/2} = \frac{5}{4}$

Q. The area bounded by y−1=∣x∣,y=0 and ∣x∣=21​ will be :

43​

23​

45​