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.

Problem 1. (Integration exercises, I) Compute the following: (a) [ tan' (0) + 1 do cos2 (0) (b) (4x - 6)v12 - 3x dx (x/2 d ( sin] x) dr () da (d) a sin' t dt (e) (*/4 1 + tan0 . do sec 0Problem 2. (Application of integrals) Answer the following questions. (a) Consider an object moving along a straight line with the velocity v(t) = 12 - 3t on [0, 6). Express the distance traveled over the given interval as a sum (or difference) of two definite integrals. (b) An oil refinery produces oil at a variable rate of A'(t) = 1000 - 10t with 0