For each of the following integrals find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral. a)x= ∫(6x2−7)3/2dx b) x= ∫x26x2+5‾‾‾‾‾‾‾√dx c) x= ∫x8x2−48x+67‾‾‾‾‾‾‾‾‾‾‾‾‾‾√dx d) x= ∫x−70−3x2+30x‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√dx

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?