Please solve these and provide justification so that I can understand and try to learn.

If you use an iPad and Apple pencil for the answer on the sheet I am showing, that is the best.

Thank you.

2) Evaluate each of the following. Explain and show your work. a) (3 points) x ("atcos(e') at VALUE: b) (4 points) ( in ( * ) d 2 x cos ( * ) dx VALUE: c) (6 points) du Veu + 3 VALUE:Math 1151 Written Homework 6 Autumn 2021 d) (3 points) Write the integral that gives the displacement of the object during the time interval [0, 2], then calculate the displacement. (Hint: You were given a formula for s(t) above.) Integral: Displacement: e) (6 points) Write the integral that gives the distance traveled by the object during the time interval [0, 2], then calculate the distance traveled Integral: Distance traveled:1) Suppose that an object moving along a straight line has position function s(t) = _2 cos(at) + # sin(wt) in meters, with t measured in hours. a) (2 points) Show that the velocity function, v(t), is equal to v(t) = 5t cos(at). b) (4 points) Explain what _v(t) d't represents and find its value on the interval [0, 2]. (Don't forget units.) VALUE : c) (2 points) Circle ALL the correct statements about the function s, or write "NONE". A . s ( t ) = 2 + v ( t ) dt C. s (1 ) = v ( x ) dx E. s(t) = s(0) + v(x) dx B. s (t ) = 2 + v ( x ) dx D. s(1) - s(0) = v(x ) dx F. s( t ) = s(0 ) + v(x ) dx