The area bounded by the curve y = sec2 x, y = 0 and |x|=(π/3) is

Question

The area bounded by the curve y = sec2 x, y = 0 and |x|=(π/3) is (A) √3 sq. units (B) √2 sq. units (C) 2√3 sq. units (D) none of these

Tardigrade Admin · Accepted Answer

We have, y=sec2x and y=0 and x=(π/3), -(π/3) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/82c5221127f7cdb169a5e9b89f2a6ccc-.png" /> Required area = area of shaded region =∫ limits-π /3π /3 sec2 x dx=[tan x]-π/ 3π /3=2√3 sq. units

Q. The area bounded by the curve $y = se c^{2} x$ , $y = 0$ and $∣ x ∣ = \frac{π}{3}$ is

$3$ sq. units

$2$ sq. units

$23$ sq. units

none of these

We have, $y = se c^{2} x$ and $y = 0$ and $x = \frac{π}{3}$ , $- \frac{π}{3}$

Required area = area of shaded region
$= - π /3 \int π /3 se c^{2} x d x = [t an x]_{- π /3}^{π /3} = 23$ sq. units

Q. The area bounded by the curve y=sec2x, y=0 and ∣x∣=3π​ is

3​ sq. units

2​ sq. units

23​ sq. units