This is entire question **Transcription for Educational Website:**---**Graph Analysis:**The graph illustrates the derivative \( g'(x) \).**Mathematical Context:**Let \( f \) be the function given by \( f(x) = (\ln x)(\sin x) \). The figure below shows the graph of \( f \) for \( 0 < x \leq 2\pi \).The function \( g \) is defined by:\[ g(x) = \int_{1}^{x} f(t) \, dt \]for \( 0 < x \leq 2\pi \).**Note:** \( g'(x) = f(x) \)---**Question 14:**On what intervals, if any, is \( g \) increasing? Justify your answer.---**Graph Description:**- The graph starts at \( x = 0 \) and ends around \( x = 6 \).- It shows an oscillating behavior with peaks and troughs, indicating where the function \( f(x) \) is positive or negative.- The graph crosses the x-axis, indicating points where \( f(x) = 0 \).**Meaning in Context:**- The function \( g \) is increasing where \( f(x) \) (or \( g'(x) \)) is positive. This corresponds to intervals where the graph lies above the x-axis.--- This material helps understand the behavior of integrals and derivatives in calculus, focusing on the increasing nature of functions defined by integrals.

Name: This is entire question **Transcription for Educational Website:**---*
Uploaded: 2024-03-20T07:07:37.000Z
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Description: This is entire question **Transcription for Educational Website:**---**Graph Analysis:**The graph illustrates the derivative \( g'(x) \).**Mathematical Context:**Let \( f \) be the function given by \( f(x) = (\ln x)(\sin x) \). The figure below show