Question

$I={\int }_0^1{e}^{x^2}dx$ satisfies which of the following inequality?

• A. $0<I<1$
• B. $-1<I<1$
• C. $1<I<e$
• D. $0<I<\frac{1}{2}$

Answer 1

Answer: (C)

$1<I<e$

$I={\int }_0^1{e}^{x^2}dx$

In the interval $[0,1]$ , we know that $1<e^{x^2}<e.$

And hence, ${\int }_0^{1}1.dx<{\int }_0^1{e}^{x^2}dx<{\int }_0^{1}e.dx$

$⟹1<I<e$

Hence,answer is option-(C).