Which one of the following integrals is improper?
A) $\int _ { 0 } ^ { 2 } 2 \sqrt { x } d x$

B) $\int _ { - 2 } ^ { 2 } \frac { 1 } { x ^ { 2 } - 2 } d x$
C) $\int _ { 0 } ^ { 3 } \frac { 1 } { x + 2 } d x$
D) $\int _ { 1 } ^ { 2 } \ln x d x$
E) $\int _ { 0 } ^ { 1 } 3 ^ { x } d x$
F) $\int _ { - 2 } ^ { 2 } \frac { 1 } { x ^ { 4 } + 1 } d x$

G) $\int _ { - 5 } ^ { 5 } \frac { 1 } { x ^ { 2 } + 2 } d x$

H)None of the above

Question

Which one of the following integrals is improper?
A) $\int _ { 0 } ^ { 2 } 2 \sqrt { x } d x$

B) $\int _ { - 2 } ^ { 2 } \frac { 1 } { x ^ { 2 } - 2 } d x$ 
C) $\int _ { 0 } ^ { 3 } \frac { 1 } { x + 2 } d x$ 
D) $\int _ { 1 } ^ { 2 } \ln x d x$ 
E) $\int _ { 0 } ^ { 1 } 3 ^ { x } d x$ 
F) $\int _ { - 2 } ^ { 2 } \frac { 1 } { x ^ { 4 } + 1 } d x$

G) $\int _ { - 5 } ^ { 5 } \frac { 1 } { x ^ { 2 } + 2 } d x$

H)None of the above

Quizplus · Accepted Answer

The integral in choice B is improper because the integrand $\frac{1}{x^2-2}$ has a discontinuity within the interval of integration $[-2, 2]$, specifically at the points where $x^2 - 2 = 0$, which are $x = \sqrt{2}$ and $x = -\sqrt{2}$. This causes the function to be undefined at these points, making the integral improper.

Which One of the Following Integrals Is Improper? A) ∫022xdx\int _ { 0 } ^ { 2 } 2 \sqrt { x } d x∫02​2x​dx

Which One of the Following Integrals Is Improper?
A) $\int _ { 0 } ^ { 2 } 2 \sqrt { x } d x$