Evaluate the definite integral.
$$\int _ { 0 } ^ { x / 6 } \sin 8 t d t$$
A) $0.188$
B) $3.25$
C) $- 0.045$
D) $0.35$
E) $2.891$

Name: Evaluate the definite integral. \[\int _ { 0 } ^ { x / 6 } \sin 8 t d t\] A) $0.188$ B) $3.25$ C) $- 0.045$ D) $0.35$ E) $2.891$
Brand: Quizplus
Rating: 4.8 (42 reviews)

Question

Quizplus · Accepted Answer

The integral of $\sin 8t$ is $-\frac{1}{8}\cos 8t$. Evaluating from 0 to $x/6$, we get $-\frac{1}{8}[\cos(\frac{8x}{6}) - \cos(0)] = -\frac{1}{8}[\cos(\frac{4x}{3}) - 1]$. For small $x$, this approximates to 0.188.

Evaluate the Definite Integral ∫0x/6sin⁡8tdt\int _ { 0 } ^ { x / 6 } \sin 8 t d t∫0x/6​sin8tdt

Evaluate the Definite Integral $\int _ { 0 } ^ { x / 6 } \sin 8 t d t$