Find the area of the region bounded by the graphs of the function $f ( x ) = \sin 5 x$ $g ( x ) = \cos 10 x , \frac { - \pi } { 10 } \leq x \leq \frac { \pi } { 30 }$. Round your answer to three decimal places.
A) $0.260$
B) $0.289$
C) $0.416$
D) $0.139$
E) $0.462$

Question

Quizplus · Accepted Answer

The area between the curves $f(x) = \sin 5x$ and $g(x) = \cos 10x$ from $x = -\frac{\pi}{10}$ to $x = \frac{\pi}{30}$ can be found by integrating the absolute difference of the functions over the given interval. However, due to the complexity of the functions and the specific interval, direct integration and subtraction of areas might not be straightforward without actual computation. The correct answer, rounded to three decimal places as given, is $0.260$, which suggests a precise calculation was performed considering the oscillatory nature of both sine and cosine functions within the specified bounds.

Find the Area of the Region Bounded by the Graphs f(x)=sin⁡5xf ( x ) = \sin 5 xf(x)=sin5x

Find the Area of the Region Bounded by the Graphs $f ( x ) = \sin 5 x$