If I (1) = int (0) ^(1) 2 ^(x ^(2)) dx, ...

If `I _(1) = int _(0) ^(1) 2 ^(x ^(2)) dx, I _(2) = int _(0) ^(1) 2 ^(x ^(3)) dx, I _(3) = int _(1) ^(2) 2 ^(x ^(3)) dx and I _(4 ) = int _(1) ^(2) 2 ^(x ^(3))` dx then-

`I _(2) gt I _(1)`

`I _(1) gt I _(2)`

`I _(3) =I_(4)`

`I _(3) gt I _(4)`

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If I_(1)=int_(0)^(1) 2^(x^(2)) dx, I_(2)=int_(0)^(1) 2^(x^(3)) dx, I_(3)=int_(1)^(2) 2^(x^(2))dx and I_(4)=int_(1)^(2) 2^(x^(2))dx then

Let I _(1) = int _(1) ^(2) (dx )/(sqrt(1 + x ^(2))) and I _(2) = int _(1) ^(2) (dx)/(x)

If I_(1) int_(1)^(2) dx/sqrt(1+x^(2)) and I_(1) = int _(1)^(2) dx/x then

IfI_(1)=int_(0)^(1)2^(x^(2)),I_(2)=int_(0)^(1)2^(x^(3))dx,I_(3)=int_(1)^(2)2^(x^(2))dx,I_(4)=int_(1)^(2)2^(x^(3))dx then which of the following is/are true? I_(1)>I_(2)(b)I_(2)>I_(1)I_(3)>I_(4)(d)I_(3)

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^(-x^(1//2)x^(2))dx . The greatest of these integrals, is

I=int_(0)^(1)((1+x)/(2-x))dx

If I_(1) =int _(0)^(1) (1+x ^(8))/(1+x^(4)) dx sand I_(2)=int _(0)^(1) (1+ x ^(9))/(1+x ^(2)) dx, then:

l_(1)=int_(0)^(1)3^(x^(2))dx,l_(2)=int_(0)^(1)3^(x^(3))dx,l_(3)=int_(1)^(2)3^(x^(2))dx,l_(4)=int_(1)^(2)3^(x^(3))dx then (i)I_(1)>I_(2)(ii)I_(2)>I_(1)(iii)I_(3)>I_(4)(iv)I_(4)>I_(3)

MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)

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