If I1=∫1e−xcos2⁡xdx, l2=∫e−x2cos2⁡xdx and I3=∫01 e−x3dx  then

If I1=1excos2xdx, l2=ex2cos2xdx and I3=01ex3dx  then

  1. A

    l3>l1>l2

  2. B

    l2>l3>l1

  3. C

    I2>I1>l3

  4. D

    I3>I2>I1

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    Solution:

    For, 0<x<1,x3<x2<x

    i.e., x3>x2>xex3>ex2>ex

     excos2x<ex2cos2x<ex3cos2x

    As cos2x1 we have ex2cos2x<ex3

    Thus, excos2x<ex2cos2x<ex3I1<I2<I3

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