Let $a$ and $b$ be real numbers. What integral must appear in place of the question mark "?" to make the following statement true?
$$\int _ { - \infty } ^ { a } \frac { 10 } { x ^ { 2 } + 9 } d x + \int _ { a } ^ { \infty } \frac { 10 } { x ^ { 2 } + 9 } d x = ? + \int _ { \partial } ^ { \infty } \frac { 10 } { x ^ { 2 } + 9 } d x$$
A) $\int _ { - \infty } ^ { a } \frac { 9 } { x ^ { 2 } + 10 } d x$
B) $\int _ { 0 } ^ { - \infty } \frac { 10 } { x ^ { 2 } - 9 } d x$
C) $\int _ { - \infty } ^ { b } \frac { 10 } { x ^ { 2 } + 9 } d x$
D) $\int _ { b } ^ { - \infty } \frac { 10 } { x ^ { 2 } + 9 } d x$
E) none of these

Question

Quizplus · Accepted Answer

The integral on the left-hand side is the sum of two integrals, each of which is an improper integral. The first integral is improper at $a$, and the second integral is improper at $\infty$. To make the statement true, the integral on the right-hand side must also be an improper integral. The only choice that is an improper integral is C.

Let aaa And bbb Be Real Numbers A) ∫−∞a9x2+10dx\int _ { - \infty } ^ { a } \frac { 9 } { x ^ { 2 } + 10 } d x∫−∞a​x2+109​dx

Let $a$ And $b$ Be Real Numbers A) $\int _ { - \infty } ^ { a } \frac { 9 } { x ^ { 2 } + 10 } d x$