Evaluate the Integral $\int _ { 0 } ^ { \ln 3 } \mathrm { e } ^ { - \mathrm { t } } \sinh \mathrm { tdt }$

question 37

Multiple Choice

Evaluate the integral.
- $\int _ { 0 } ^ { \ln 3 } \mathrm { e } ^ { - \mathrm { t } } \sinh \mathrm { tdt }$

• A) \(\ln \frac { 3 } { 2 } - \frac { 2 } { 9 }\)
• B) \(\frac { \ln 3 } { 2 } + \frac { 1 } { 36 }\)
• C) \(\frac { \ln 3 } { 2 } + 2\)
• D) \(\frac { \ln 3 } { 2 } - \frac { 2 } { 9 }\)

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Definitions:

Antagonist

In pharmacology and physiology, an antagonist is a substance that blocks or dampens the effects of a neurotransmitter or hormone; in literature, it describes a character that opposes the protagonist.

Hip Flexor

A group of muscles near the hip that are involved in moving the upper leg towards the body.

Semitendinosus

A muscle in the thigh that helps to flex the knee and extend the hip.

Rectus Femoris

One of the four quadriceps muscles of the thigh, it extends the knee and helps flex the hip.