JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Hard

1 of 1

Analyzing +4 | -1

Let

I_{1}=\int_{0}^{\pi / 2} e^{-x^{2}} \sin (x) d x ; I_{2}=\int_{0}^{\pi / 2} e^{-x^{2}} d x ; I_{3}=\int_{0}^{\pi / 2} e^{-x^{2}}(1+x) d x

and consider the statements

I.

{I}_{1}<{I}_{2}

\quad

II.

{I}_{2}<{I}_{3}

\quad

III.

{I}_{1}={I}_{3}

Which of the following is(are) true?

View answer and explanation

Correct option: D

Both I and II

Option D (Both I and II) is correct because in the interval (0, π/2), 0 < sin(x) < 1 and 1+x > 1, leading to the inequalities I1 < I2 < I3.

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