Question

Area of the region bounded by the y-axis, y = \sin x, when 0 \le x \le \tfrac{\pi}{4}, is

• A. sq. units
• B. $\sqrt{2}-1$ sq. units
• C. $\sqrt{2}-1$ sq. units
• D. $\sqrt{2}+1$ sq. units

Answer 1

Answer: (B)

$\sqrt{2}-1$ sq. units

Answer 2

We compute the area

$$A = \int_{0}^{\pi/4} \sin x \,dx = \bigl[-\cos x\bigr]_{0}^{\pi/4} = -\cos\!\bigl(\tfrac{\pi}{4}\bigr) + \cos(0) = -\tfrac{\sqrt{2}}{2} + 1 = 1 - \tfrac{\sqrt{2}}{2} = \sqrt{2}-1.$$