`IfI_1=int_0^1 2x ,I_2=int_0^1 2^x^3dx ,I_3=int_1^22^x^2dx ,I_4=int_1^2 2^x^3dx ,` then which of the following is/are ture? `I_1> I_2` (b) `I_2> I_2`

Monjur Alahi

`IfI_1=int_0^1 2x ,I_2=int_0^1 2^x^3dx ,I_3=int_1^22^x^2dx ,I_4=int_1^2 2^x^3dx ,` then which of the following is/are ture? `I_1> I_2` (b) `I_2> I_2` `I_3> I_4` (d) `I_3A. `I_(1)gtI_(2)`
B. `I_(2)gtI_(1)`
C. `I_(3)gtI_(4)`
D. `I_(3)ltI_(4)`


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Salim Ahmed Kawsar

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Correct Answer - A::D
For `0lt xlt 1, x^(3)gtx^(3)`
or `2^(x^(2))gt2^(x^(3))`
or `int_(0)^(1)2^(x^(2))dxgt int_(0)^(1)2^(x^(3))dx`
Hence `I_(1)gtI_(2)`
Also for `1ltxlt2, x^(2)ltx^(3)`
or `2^(x^(2))lt2^(x^(3))`
or `int_(1)^(2)2^(x^(2))dxlt int_(1)^(2)2^(x^(3))dx`
or `I_(3)ltI_(4)`

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