Evaluate the improper integral.
-$$\int _ { 2 } ^ { 38 } \int _ { 1 } ^ { 50 } \frac { \mathrm { dxdy } } { \sqrt { ( \mathrm { x } - 1 ) ( \mathrm { y } - 2 ) } }$$
A) 210
B) 252
C) 126
D) 168

Question

Quizplus · Accepted Answer

First, we use a change of variable $x-1=u^2$, $y-2=v^2$ to get:
$$\int_0^6\int_0^7\frac{1}{2}u^{-1}v^{-1}\,du\,dv$$
Then we separate it into two integrals:
$$\int_0^6u^{-1}\,du\int_0^7v^{-1}\,dv$$
$$=\ln(6)\ln(7)=\ln(42^{\frac{1}{2}}\cdot7^{\frac{1}{2}})=\ln(84)$$
$$=D$$

Evaluate the Improper Integral ∫238∫150dxdy(x−1)(y−2)\int _ { 2 } ^ { 38 } \int _ { 1 } ^ { 50 } \frac { \mathrm { dxdy } } { \sqrt { ( \mathrm { x } - 1 ) ( \mathrm { y } - 2 ) } }∫238​∫150​(x−1)(y−2)​dxdy​

Evaluate the Improper Integral $\int _ { 2 } ^ { 38 } \int _ { 1 } ^ { 50 } \frac { \mathrm { dxdy } } { \sqrt { ( \mathrm { x } - 1 ) ( \mathrm { y } - 2 ) } }$