Solve this: If I1=∫01e-xcos2xdx,I2=∫01e-x2cos2xdx andI3=∫01e-x3dx;then:1 I3 I1 I22 I2 I3 I13 I3 I2 I14 I2 I1 I3 - Maths - Integrals

Question

Solve this:
I f   I 1 = ∫ 0 1 e - x cos 2 x d x , I 2 = ∫ 0 1
e - x 2 cos 2 x d x   a n d I 3 = ∫ 0 1 e - x 3 d x ; t
h e n : 1 I 3 > I 1 > I 2 2 I 2 > I 3 > I 1 3 I 3 >
I 2 > I 1 4 I 2 > I 1 > I 3

Neha Sethi · Accepted Answer

Dear student I1=∫01e-xcos2x dxI2=∫01e-x2cos2x dxI3=∫01e-x3 dxFor 0-x⇒e-x2>e-x⇒e-x2 cos2x>e-x cos2x⇒∫01e-x2 cos2x dx>∫01e-x cos2x dx and cos2x≤1⇒∫01e-x2 cos2x dx<∫01e-x3 dxSo, ∫01e-x3 dx>∫01e-x2 cos2x dx>∫01e-x cos2x dx I3>I2>I1 Regards

Solve this: I f I 1 = ∫ 0 1 e - x cos 2 x d x , I 2 = ∫ 0 1 e - x 2 cos 2 x d x a n d I 3 = ∫ 0 1 e - x 3 d x ; t h e n : 1 . I 3 > I 1 > I 2 2 . I 2 > I 3 > I 1 3 . I 3 > I 2 > I 1 4 . I 2 > I 1 > I 3

Solve this:
$I f I_{1} = \int_{0}^{1} e^{- x} \cos^{2} x d x, I_{2} = \int_{0}^{1} {e^{- x}}^{2} \cos^{2} x d x a n d I_{3} = \int_{0}^{1} e^{- x^{3}} d x; t h e n : 1 . I_{3} > I_{1} > I_{2} 2 . I_{2} > I_{3} > I_{1} 3 . I_{3} > I_{2} > I_{1} 4 . I_{2} > I_{1} > I_{3}$