Use the substitution formula to evaluate the integral.
-$$\int _ { - 2 / 5 } ^ { - \sqrt { 2 / 5 } } \frac { d t } { t \sqrt { 25 t ^ { 2 } - 1 } }$$
A) $- \frac { \pi } { 12 }$
B) $- \frac { \pi } { 6 }$
C) $\frac { \pi } { 12 }$
D) $\frac { \pi } { 6 }$

Question

Quizplus · Accepted Answer

The integral can be solved by using the substitution $t = \frac{1}{5}\sec(\theta)$, which simplifies the integral into a form that directly relates to the inverse trigonometric function $\sec^{-1}(x)$, leading to the solution $-\frac{\pi}{12}$.

Use the Substitution Formula to Evaluate the Integral ∫−2/5−2/5dtt25t2−1\int _ { - 2 / 5 } ^ { - \sqrt { 2 / 5 } } \frac { d t } { t \sqrt { 25 t ^ { 2 } - 1 } }∫−2/5−2/5​​t25t2−1​dt​

Use the Substitution Formula to Evaluate the Integral $\int _ { - 2 / 5 } ^ { - \sqrt { 2 / 5 } } \frac { d t } { t \sqrt { 25 t ^ { 2 } - 1 } }$