 # Which of the following integrals are improper integrals? 1. int_0^3(3-x)^2 3dx 2. int_1^16 (e^sqrtx)/sqrtx dx fortdefruitI 2020-12-05 Answered

Which of the following integrals are improper integrals?
1.${\int }_{0}^{3}{\left(3-x\right)}^{2}\left\{3\right\}dx$
2.${\int }_{1}^{16}\frac{{e}^{\sqrt{x}}}{\sqrt{x}}dx$
3.${\int }_{1}^{\mathrm{\infty }}\frac{3}{\sqrt{x}}dx$
4.${\int }_{-2}^{2}3{\left(x+1\right)}^{-1}dx$
a) 1 only
b)1 and 2
c)3 only
d)2 and 3
e)1,3 and 4
f)All of the integrals are improper

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Step 1
Given,
Improper integrals.
Step 2
Now,
The improper integrals are those integrals which has a infinite intervals of integration and integrals with discontinuous integrands in the section.
So, from the options, we have
The integral ${\int }_{1}^{\mathrm{\infty }}\frac{3}{\sqrt{x}}dx$ has infinite intervals.
The integral ${\int }_{1}^{\mathrm{\infty }}\frac{3}{\sqrt{x}}dx$ is improper integral.
$\therefore$ Option (C) is correct.