1. Tardigrade
  2. Question
  3. Mathematics
  4. Let I1=∫ limits0π / 2 e-x2 sin (x) d x ; I2=∫ limits0π / 2 e-x2 d x ; I3=∫ limits0π / 2 e-x2(1+x) d x and consider the statements text I I 1< I 2 text II I 2< I 3 text III I 1= I 3 Which of the following is(are) true?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $I_1=\int \limits_0^{\pi / 2} e^{-x^2} \sin (x) d x ; I_2=\int\limits_0^{\pi / 2} e^{-x^2} d x ; I_3=\int\limits_0^{\pi / 2} e^{-x^2}(1+x) d x$ and consider the statements
$\text { I } I _1< I _2$
$\text { II } I _2< I _3 $
$\text { III } I _1= I _3$
Which of the following is(are) true?

Integrals

Solution:

since $0< \sin x< 1$ and $1+x >1$ in $(0, \pi / 2)$
hence $I _3> I _2> I _1$
$\Rightarrow \text { A and B are correct } \Rightarrow \text { (D) }$