Which one of the following is not an improper integral?
A) $\int _ { - 4 } ^ { 2 } \frac { 1 } { x + 2 } d x$

B) $\int _ { - 2 } ^ { 2 } \frac { 1 } { x ^ { 2 } - 2 } d x$
C) $\int _ { 0 } ^ { \infty } \frac { 1 } { x + 2 } d x$

D)
$\int _ { - 2 } ^ { 2 } \frac { 1 } { x ^ { 2 } + 2 } d x$
E) $\int _ { - \infty } ^ { 1 } \frac { 1 } { x - 2 } d x$
F) $\int _ { - 2 } ^ { 2 } \frac { 1 } { x + 2 } d x$

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

H) $\int _ { - 2 } ^ { 2 } \frac { 1 } { x - 2 } d x$

Question

Which one of the following is not an improper integral?
A) $\int _ { - 4 } ^ { 2 } \frac { 1 } { x + 2 } d x$

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

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

H) $\int _ { - 2 } ^ { 2 } \frac { 1 } { x - 2 } d x$

Quizplus · Accepted Answer

An improper integral involves integration over an infinite interval or an integrand that approaches infinity within the interval of integration. Choice D, $\int _ { - 2 } ^ { 2 } \frac { 1 } { x ^ { 2 } + 2 } d x$, does not have an infinite interval nor does the integrand approach infinity within the interval, making it a proper integral.

Which One of the Following Is Not an Improper Integral ∫−421x+2dx\int _ { - 4 } ^ { 2 } \frac { 1 } { x + 2 } d x∫−42​x+21​dx

Which One of the Following Is Not an Improper Integral $\int _ { - 4 } ^ { 2 } \frac { 1 } { x + 2 } d x$