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Question

Question: I<sub>1</sub> = \(\int_{0}^{\pi/2}{\sin xdx},\) I<sub>2</sub> = \(\int_{0}^{\pi/2}{\sin^{3}xdx}\), t...

I1 = 0π/2sinxdx,\int_{0}^{\pi/2}{\sin xdx}, I2 = 0π/2sin3xdx\int_{0}^{\pi/2}{\sin^{3}xdx}, then -

A

I1> I2

B

I1< I2

C

I1 = I2

D

I2 = 0

Answer

I1> I2

Explanation

Solution

Q 0 < x < p/2 Ž sin x > sin3x

Ž 0π/2sinxdx>0π/2sin3xdx\int_{0}^{\pi/2}{\sin xdx > \int_{0}^{\pi/2}{\sin^{3}xdx}} Ž I1 > I2