7
$$f ( x ) = 2 + \cos x + 3 \sin x$$
- Express \(\mathrm { f } ( x )\) in the form
$$\mathrm { f } ( x ) = a + b \cos ( x - c )$$
where \(a , b\) and \(c\) are constants, \(b > 0\) and \(0 < c < \frac { \pi } { 2 }\).
- Solve the equation \(\mathrm { f } ( x ) = 0\) for \(x\) in the interval \(0 \leq x \leq 2 \pi\).
- Use Simpson's rule with four strips, each of width 0.5 , to find an approximate value for
$$\int _ { 0 } ^ { 2 } f ( x ) d x$$