Evaluate the improper integral $\int _ { 0 } ^ { 4 } \frac { 1 } { 4 - x } d x$
A) $\frac { \pi } { 2 }$

B) $\frac { \pi } { 4 }$

C) $\pi$
D) $\frac { 3 } { 2 }$
E) $\frac { \pi } { 16 }$
F) $\frac { \pi } { 8 }$
G)1
H)Divergent

Question

Evaluate the improper integral $\int _ { 0 } ^ { 4 } \frac { 1 } { 4 - x } d x$ 
A) $\frac { \pi } { 2 }$

B) $\frac { \pi } { 4 }$

C) $\pi$ 
D) $\frac { 3 } { 2 }$ 
E) $\frac { \pi } { 16 }$ 
F) $\frac { \pi } { 8 }$ 
G)1
H)Divergent

Quizplus · Accepted Answer

The integral $\int _ { 0 } ^ { 4 } \frac { 1 } { 4 - x } d x$ is improper because the integrand becomes undefined at $x = 4$. Evaluating the integral involves a limit process as $x$ approaches 4 from the left, which leads to an infinite discontinuity. Thus, the integral is divergent.

Evaluate the Improper Integral ∫0414−xdx\int _ { 0 } ^ { 4 } \frac { 1 } { 4 - x } d x∫04​4−x1​dx

Evaluate the Improper Integral $\int _ { 0 } ^ { 4 } \frac { 1 } { 4 - x } d x$