If I 1 - - 0 1 e - x cos 2 x d x -I 2 - - 0 1 e - x 2 cos 2 x d x - I 3 - - 0 1 e - x 3 d x - then -

The correct option is A I _ 2 > I _ 3 > I _ 1 I_1 = ∫_0^1 e^ xcos^2 x .dx I_2 = ∫_0^1 e^ x^2cos^2 x .dx I_3 = ∫_0^1 e^ x^3 dx upo ...

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Basic Trigonometric Identities

If I 1 = ∫...

Question

If $I_{1} = \int_{0}^{1} e^{- x} {cos}^{2} x d x, I_{2} = \int_{0}^{1} e^{- x^{2}} {cos}^{2} x d x, I_{3} = \int_{0}^{1} e^{- x^{3}} d x; then :$

I_{2} > I_{3} > I_{1}

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I_{2} > I_{1} > I_{3}

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I_{3} > I_{2} > I_{1}

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I_{3} > I_{1} > I_{2}

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Solution

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Similar questions

I_{1} = 1 \int 0 e^{- x} {cos}^{2} x d x

I_{2} = 1 \int 0 e^{- x^{2}} {cos}^{2} x d x

I_{3} = 1 \int 0 e^{- x^{3}} d x

I_{1} = \int_{0}^{1} e^{- x^{2}} d x, I_{2} = \int_{0}^{1} e^{- x} {cos}^{2} x d x

I_{3} = \int_{0}^{1} e^{- x^{2}} {cos}^{2} x d x .

I_{1} = \int_{0}^{1} e^{- x} c o s^{2} x d x

I_{2} = \int_{0}^{1} e^{- x^{2}} c o s^{2} x d x, I_{3} = \int_{0}^{1} e^{- x^{2}} d x

I_{4} = \int_{0}^{1} e^{- (1 / 2) x^{2}} d x

I

I_{1} = π / 2 \int 0 cos (sin x) d x; I_{2} = π / 2 \int 0 sin (cos x) d x

I_{3} = π / 2 \int 0 cos x d x,

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

I_{3} = \int_{0}^{1} e^{- x^{2}} d x

I_{4} = \int_{0}^{1} e^{\frac{- x^{2}}{2}} d x

I_{4}

\int_{a}^{b} f (x) d x < \int_{a}^{b} g (x) \forall f (x) \geq g (x)

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