Hello,

I am confirming my assignment answers and looking to get a hundred on this. Please point out every single mistake I made on this.

Thank you :)

1. Find the general antiderivative, F(x), for the given functions. a) f(x) =-sin' xcosx = _ ws sinx x ( 2 ) - U- sink, du cost let it . due b) f ( x ) = 17 - 2x 2 ) ( 7- 2 x ) /2 dx lost 3 - - 4. sinLA) . - bin't + 6 2 1: 5 - ( 7 24 ) 1 2 +C. 2. Solve the following indefinite integrals, using substitution or integration by parts where needed (3 marks each - 9 marks total) a ) [x(4+x2 ) do b) 1 - 1 + 4 x -1 /2 VItx+ 2x2 - du- 2 x dx = edx . clu 2 x $ 4:2* + + +1 -cher, yx tidx = elx, la 1/ x + 1 1 . "" 11 - 1. ( 4+x2 ) " ( 4 ) + C 1/2 ( 4 + + 2 + C 22 L - 2 ( 24 7 4 X41 ) +6 - 2 V24 +4 +1 +6.askedx - integrate by parts. [ Fg - $4- ) 84 " Fuln (4 ) , 84 19: 42 14.-4 In( ) +1 A x X 3. Solve the differential equation =-3cosx -4x? if y(x) =0. do (2) when y ( TT ) = 1 7 - 3 sin Lli ) - 4 (ro ) 3 3 3 7 4 ( + ) .- 3 sin( )-yx 3 zy ( x ) - - 95 in ( x ) -42 14 y (x ) = 47 7 - 9 9in (+ ) - 4 + 3 3 3 4. A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of 12 m/s. With what velocity does the stone hit the ground? Assume acceleration due to gravity is - 9.8 m/ $2 . Round to the nearest tenth. ( 3 ) 7- 4.4/2 + 121 + c- 5- - 4.4 (D) + 12(0) +0 -5 - 6-,5 2 ( - 4.9) 27x, - 2. 8418), X2: - 0136 4 Extraneous root . x- 2. Past. w /+ ) = - 4.7+ + 12 - v ( 2.3187) .- 9.2 (2.9187) +12 - 4(+ ) . - 15. 6 mls ) Negative because falling down?5. Find the area of the region enclosed by the parabolas y = x and y= shade in the region of interest. Show all work including finding intersection points. (4) Point of intersections , at that -2x- 0 17 74 - 2+ 0 - 24( x-1)-0 POE (0, 0), (1,1). (1,1 ) (0,0 - D 3 6. Find the area bounded by the curves y = sinx and y = cosx from x =0 tox = 7 . Make a sketch and shade in the region of interest. Give an exact value answer. (4) 4 ,0.7 ) Vosint is - A= ( cost - sind ) dx + [ ( sint - cost ) dot Alsink+cost) + [-cosx - sink Jayy