Question

2. Let $x$ and $y$ be real numbers be such $x, y \in \{\frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}, \frac{2\pi}{3}, \pi\}$. (a) If $\int_0^x 4\cos^4(2t)dt = \frac{3\pi}{2}$, find $x$. Hint: Use the table below Let $f(x) = \frac{3}{2}x + \frac{1}{2}\sin(4x) + \frac{1}{16}\sin(8x) - \frac{3\pi}{2}$. $\begin{array}{|c|c|} \hline x & f(x) \\ \hline \frac{\pi}{6} & -3.5481 \\ \frac{\pi}{4} & -3.5343 \\ \frac{\pi}{3} & -3.5205 \\ \frac{\pi}{2} & -2.3562 \\ \frac{2\pi}{3} & 2.35619 \\ \pi & 0 \\ \hline \end{array}$

          2. Let $x$ and $y$ be real numbers be such $x, y \in \{\frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}, \frac{2\pi}{3}, \pi\}$.
(a) If
$\int_0^x 4\cos^4(2t)dt = \frac{3\pi}{2}$, find $x$.
Hint: Use the table below
Let $f(x) = \frac{3}{2}x + \frac{1}{2}\sin(4x) + \frac{1}{16}\sin(8x) - \frac{3\pi}{2}$.
$\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
\frac{\pi}{6} & -3.5481 \\
\frac{\pi}{4} & -3.5343 \\
\frac{\pi}{3} & -3.5205 \\
\frac{\pi}{2} & -2.3562 \\
\frac{2\pi}{3} & 2.35619 \\
\pi & 0 \\
\hline
\end{array}$

$2. Let x and y be real numbers be such x, y ∈{(π)/(6), (π)/(4), (π)/(3), (π)/(2), (2π)/(3), π}. (a) If ∫0^x 4cos^4(2t)dt = (3π)/(2), find x. Hint: Use the table below Let f(x) = (3)/(2)x + (1)/(2)sin(4x) + (1)/(16)sin(8x) - (3π)/(2). x f(x) (π)/(6) -3.5481 (π)/(4) -3.5343 (π)/(3) -3.5205 (π)/(2) -2.3562 (2π)/(3) 2.35619 π 0$

Added by Cheryl N.

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