The area bounded by the curve y=| cos x- sin x|, 0 ≤ x ≤ (π/2) and above x-axis is

Question

The area bounded by the curve y=| cos x- sin x|, 0 ≤ x ≤ (π/2) and above x-axis is (A) 2 √2 (B) 2 √2-2 (C) 2 √2+1 (D) 2 √2+2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/342971913e35f8e7a781540b7bc6e703-.png" /> So, required area =∫ limits0π / 4( cos x- sin x) d x+∫ limitsπ / 4π / 2-( cos x- sin x) d x=2(√2-1)

Q. The area bounded by the curve $y = ∣ cos x - sin x ∣, 0 \leq x \leq \frac{π}{2}$ and above $x$ -axis is

$22$

$22 - 2$

$22 + 1$

$22 + 2$

So, required area $= 0 \int π /4 (cos x - sin x) d x + π /4 \int π /2 - (cos x - sin x) d x = 2 (2 - 1)$

Q. The area bounded by the curve y=∣cosx−sinx∣,0≤x≤2π​ and above x-axis is

22​

22​−2

22​+1

22​+2