Use the Table of Integrals to Evaluate the Integral $\int e^{4 x} \sin 2 x d x$

question 107

Multiple Choice

Use the Table of Integrals to evaluate the integral. $\int e^{4 x} \sin 2 x d x$

• A) \(-\frac{1}{5} e^{4 x} \sin 2 x+\frac{1}{10} e^{4 x} \cos 2 x+C\)
• B) \(\frac{1}{5} e^{4 x} \sin 2 x+\frac{1}{10} e^{4 x} \cos 2 x+C\)
• C) \(\frac{1}{5} e^{4 x} \sin 2 x-\frac{3}{10} e^{4 x} \cos 2 x+C\)
• D) \(-\frac{1}{5} e^{4 x} \sin 2 x-\frac{1}{10} e^{4 x} \cos 2 x+C\)
• E) \(\frac{1}{5} e^{4 x} \sin 2 x-\frac{1}{10} e^{4 x} \cos 2 x+C\)

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Definitions:

Organ of Corti

A structure in the cochlea of the inner ear that produces nerve impulses in response to sound vibrations.

Kinocilium

A specialized type of cilium on the apical surface of hair cells in the sensory epithelium of the vertebrate inner ear, crucial for the detection of sound and movement.

Basilar Membrane

A structure in the cochlea of the inner ear that supports the organ of Corti, playing a critical role in sound perception.

Cilia

Microscopic, hair-like structures on the surface of cells that move in a wave-like manner to propel substances.