Evaluate the integral.
-$$\int _ { - \ln 3 } ^ { 0 } 5 \sinh ^ { 2 } \left( \frac { x } { 2 } \right) d x$$
A) $\frac { 5 } { 3 } \left( e ^ { 6 } - e ^ { - 6 } \right)$
B) $\frac { 5 } { 2 } \left( \frac { 4 } { 3 } - \ln 3 \right)$
C) $\frac { 5 } { 2 } \left( \frac { 4 } { 3 } + \ln 3 \right)$
D) $- \frac { 320 } { 81 }$

Question

Quizplus · Accepted Answer

The integral evaluates to $\frac{5}{2} \left( \frac{4}{3} - \ln 3 \right)$ using the identity $\sinh^2(x) = \frac{1}{2}(\cosh(2x) - 1)$ and integrating.

Evaluate the Integral ∫−ln⁡305sinh⁡2(x2)dx\int _ { - \ln 3 } ^ { 0 } 5 \sinh ^ { 2 } \left( \frac { x } { 2 } \right) d x∫−ln30​5sinh2(2x​)dx

Evaluate the Integral $\int _ { - \ln 3 } ^ { 0 } 5 \sinh ^ { 2 } \left( \frac { x } { 2 } \right) d x$