Review (Beginning of Chapter 5)

Calculus Review Worksheet(1) Evaluate each of the following integrals please.∫ x + x 1 dx(k)∫3 sin( 5x ) dx2(a) ( − )∫6 7x dx(l)(b) ( − ) 3(c) 3 ( −4 ) 5(d)∫∫( − )cos x 1dxx − 1( ) ( )∫ x 5 x dx2(m) 1 − sin 1 1( x2 ) cos x dx2∫( x − 1)dx(n)∫( ) ( )x 2 − 2x + 5( ) 2(e)∫dx3 2x3x + 33x + 3 dx( )(f)∫ x(g)∫3x dx22x + 3(h)∫⎛⎜⎝2xx8+ 1⎞⎟− 3 ⎠dx( x − 3)(i) ( ⋅⋅ )2∫3 2tan 3x sec 3x dx3(o) tan( 2x ) sec ( )∫2(p) cot ( )(q)∫f (x) g'(x) + f '(x) g(x) dx (s)3(j) ( − ) 2∫∫sec2x dx2(r) cos ( π )∫( ) ( )22x dxx tan x dx( )3 + sec xx dx1 ⎛ 1 ⎞ ⎛ 1 ⎞sin cos dx3 ⎜ 2 ⎟ ⎜ 2 ⎟x ⎝ x ⎠ ⎝ x ⎠∫ x 2 dx(t)∫2( tan( x) + sec( x)) dx(2) Solve each of the following differential equations please.(a)(b)2d y 16= , the graph of y passes through (2 , 3) with slope 0.2 3dx xdy cos( πx)= , y passes through (1 , 4).dx y

(1) (a)31 3 2x + x 2 x + C3 3(b)1( ) 428 6 7x + CCalculus Review WorksheetAnswers− (k)3 cos( 5x)− + C5− − (l) sin(x 1)(c)1 4( ) 6242 − + C3− 5 − x + C(m) 2sin1( x2 1) − sin ( x)+ C(d)1 2( ) 12 x 2x + 5 + C−− − (n) tan 4 ( 3x)2 3 21 + C12(e)36 x + 3 + C (o) sec 3 ( 2x)61+ C(f)1( ) 42x + 3 + C (p) ( )− cot x – x + C(g)32222x + 3 + C (q) 3 + sec ( x ) + C(h)91 ⎛ 2x + 1⎞− ⎜ ⎟63 ⎝ x − 3 ⎠+ C(r) 1 x + 1 sin ( 2 x)2 4ππ + Ci (s) − 1 2sin⎛ 1 ⎞⎜ 2 ⎟ + C or 1 2cos⎛ 1 ⎞4⎜ ⎟ + C⎝ x ⎠ 4 2⎝ x ⎠(i) f ( x ) g( x ) + C(j)1 7 47 x x + 4x + C2tan x + 2sec x – x + C− (t) ( ) ( )(2) (a)8y = + 2x − 5x3y 2 =3 π(b)2 1 sin( πx)+163