Evaluate the improper integral.
-$$\int _ { 0 } ^ { 25 } \frac { d x } { \sqrt { | x - 16 | } }$$
A) 6
B) 7
C) 14
D) -2

Question

Quizplus · Accepted Answer

We can split the integral into two parts: 
$$\int _ { 0 } ^ { 16 } \frac { d x } { \sqrt { 16 - x } } + \int _ { 16 } ^ { 25 } \frac { d x } { \sqrt { x - 16 } }$$
For the first integral, we can substitute $u = 16-x$, which gives us
$$-\int _ { 16 } ^ 0 \frac {du}{\sqrt u} = -2\sqrt u\bigg|_{16}^0 = 2\sqrt{16} = 8$$
For the second integral, we can substitute $v = x-16$, which gives us
$$\int _ { 0 } ^ 9 \frac {dv}{\sqrt v} = 2\sqrt v\bigg|_{0}^9 = 6$$
Therefore, the total value of the integral is $8+6 = 14$.

Evaluate the Improper Integral ∫025dx∣x−16∣\int _ { 0 } ^ { 25 } \frac { d x } { \sqrt { | x - 16 | } }∫025​∣x−16∣​dx​

Evaluate the Improper Integral $\int _ { 0 } ^ { 25 } \frac { d x } { \sqrt { | x - 16 | } }$