Evaluate the improper integral.
-$$\int _ { 0 } ^ { 49 } \frac { d x } { \sqrt { 49 - x } }$$
A) 7
B) 0
C) 14
D) -14

Question

Quizplus · Accepted Answer

We can solve this using substitution.
Let $u=49-x$, then $du=-dx$
The integral becomes 
\begin{align*}
\int _ { 0 } ^ { 49 } \frac { d x } { \sqrt { 49 - x } }&=\int_{49}^0 \frac{-du}{\sqrt{u}}\
&=\int_0^{49}\frac{du}{\sqrt{u}}\
&=2\sqrt{u} \biggr|_0^{49}\
&=2\sqrt{49}-2\sqrt{0}\
&=14
\end{align*}
Therefore, the answer is (C).

Evaluate the Improper Integral ∫049dx49−x\int _ { 0 } ^ { 49 } \frac { d x } { \sqrt { 49 - x } }∫049​49−x​dx​

Evaluate the Improper Integral $\int _ { 0 } ^ { 49 } \frac { d x } { \sqrt { 49 - x } }$