Question

If I₁ = $\int_{0}^{\pi/2\int}\cos$ (sin x) dx; I₂ = $\int_{0}^{\pi/2\int}\sin$ (cos x)dx and

I₃ = $\int_{0}^{\pi/2\int}\cos$ x dx, then -

• A. I₁> I₃> I₂
• B. I₃> I₁> I₂
• C. I₁> I₂> I₃
• D. I₃> I₂> I₁

Answer 1

Answer: (A)

I₁> I₃> I₂

Answer 2

Sol. Qsinx < x " x Ī (0, )

so, cos(sin x) > cosx, so I₁ > I₃

and sin sinx > sinx

so $\int_{0}^{\pi/2}{\sin(\sin x)dx}$ > $\int_{0}^{\pi/2}{(\sin x)dx}$

$\int_{0}^{\pi/2}{\sin(\cos x)dx}$> $\int_{0}^{\pi/2}{(\cos x)dx}$Ž I₂ > I₃