Question

The area bounded by the curves $y=\sin x,y=$ cosx and the $y$-axis and the first point of intersection is:

• A. $\sqrt{2}$ sq,.units
• B. $\sqrt{2}-1$ sq. units
• C. $2+\sqrt{2}$ sq. units
• D. 0 sq, units

Answer 1

Answer: (B)

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

$\stackrel{\pi /4}{\underset{0}{\int }}(\cos x-\sin x)dx$
$\stackrel{\pi /4}{\underset{0}{\int }}\cos xdx-\stackrel{\pi /4}{\underset{0}{\int }}\sin xdx$
$\sin x{|}_0^{\pi /4}+\cos x{|}_0^{\pi /4}$
$=1/\sqrt{2}+1/\sqrt{2}-1$
$=\sqrt{2}-1squnits.$