Let I(1)=int(0)^(pi//4)e^(x^(2))dx, I(2)...

Let `I_(1)=int_(0)^(pi//4)e^(x^(2))dx, I_(2) = int_(0)^(pi//4) e^(x)dx, I_(3) = int_(0)^(pi//4)e^(x^(2)).cos x dx`, then :

`I_(1)gt I_(2)gt I_(3)gt I_(4)`

`I_(2)gt I_(3)gt I_(4)gt I_(1)`

`I_(3)gt I_(4)gt I_(1)gt I_(2)`

`I_(2)gt I_(1)gt I_(3)gt I_(4)`

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If I_(1)=int_(0)^(pi//2) cos(sin x) dx,I_(2)=int_(0)^(pi//2) sin (cos x) dx and I_(3)=int_(0)^(pi//2) cos x dx then

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I_(1)=int_(0)^((pi)/2)Ln (sinx)dx, I_(2)=int_(-pi//4)^(pi//4)Ln(sinx+cosx)dx . Then

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Let I_(1) = int_(0)^(pi/4)x^(2008)(tanx )^(2008)dx, I_(2) = int_(0)^(pi/4) x ^(2009)(tan x)^(2009)dx , I_(3) = int_(0)^(pi/4) x^(2010)(tanx)^(2010)dx then which one of the following inequalities hold good?

Consider the integrals I_(1)=int_(0)^(1)e^(-x)cos^(2)xdx,I_(2)=int_(0)^(1) e^(-x^(2))cos^(2)x dx,I_(3)=int_(0)^(1) e^(-x^(2))dx and I_(4)=int_(0)^(1) e^(-(1//2)x^(2))dx . The greatest of these integrals, is

(i) int_(0)^(pi//2) x sin x cos x dx (ii) int_(0)^(pi//6) (2+3x^(2)) cos 3x dx

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