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I_n = \int (0 to n*pi) sinxdx/(1+x)

Source: ISI BS 2011, P8

March 31, 2013
integrationtrigonometrycalculuscalculus computations

Problem Statement

Let In=∫0nπsin⁡x1+x dx,    n=1,2,3,4I_n =\int_{0}^{n\pi} \frac{\sin x}{1+x} \, dx , \ \ \ \ n=1,2,3,4 Arrange I1,I2,I3,I4I_1, I_2, I_3, I_4 in increasing order of magnitude. Justify your answer.
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