The area bounded by the y-axis, y= x and y= x, when 0≤ x≤()/4, is Option 1: √2 Option 2: √2+1 Option 3: √2-1 Option 4: (√2-1)/2

Answer: √2-1. Solution: On [0,()/4], x≥ x. Area =_0^(/4)( x- x)dx=[ x+ x]_0^(/4)=2-1.

Calculus

Application of Integrals

Easy

core

The area bounded by the y-axis, $y=\cos x$ and $y=\sin x$ , when $0\leq x\leq\frac{\pi}{4}$ , is

$\sqrt{2}$

$\sqrt{2}+1$

$\sqrt{2}-1$

$\frac{\sqrt{2}-1}{2}$

✅ Correct Option: 3

On $\left[0,\frac{\pi}{4}\right]$ , $\cos x\ge\sin x$ . Area $=\int_0^{\pi/4}(\cos x-\sin x)dx=[\sin x+\cos x]_0^{\pi/4}=\sqrt2-1$ .

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