Question

The graph of f is shown below. Find each of the following:

ДА 9 10 11 12 13 14 15 15 a) | 4e** f(e?*)dx ja b) [2]5(-x+1) di c) [°50f(3x² +1)dx + d) 3f (2 cos(4x)+1) .dk csc(4x) (Vx √x - dx f) s f (5 tan(3x)) - dx cos? (3x) +1+ 12

Answer 1

2 lnz we get PAGE 1 I lns Apply substitution method J + 2x f ( 22x) dx , Let e 2x = t or e2%2dx=dt swestituting in egn. we get Sas(A) It Also changing the limits of integration Lower limit as 2 upper limitas t= et ln2=2 t=ahen5=5 :./24 (6) at = 2 [£x 2x6 + 2x6] = 12 sg. Units [Apply triangle formula 1 x G x h] Rectangle formula expl (6) J2lfExH) / dx ; Apply substitution method Let -x+1=t-dx=dt of Salf (el (dt) when x=-1;t=2 when = 4; t = -3 / 21 fuldt or Jal Fieldt 1248683) at + Szffwldt + 52 1208, dat o, [2x3+4x1X3 + 4x2x3] on, [6+.5 +3] = 10.5sq.m -3 2 -3 units.

2 4 Page 2 (E) i sxf (3271) dx Let 3x²+1=t Gxdx = dt os, 5xdx=set 4 is at fit) = f sceidet - Axelt + (3) Sorende 0 {4x1x 3+ 4 x2x6] 82, £[|-5 +0] = -5X75 -5x7,5 26:25 (Ignoring negative sign) (do 576 3 F (265 (42) 70 dx Let 2 cos (4x)+1=t CSL (4x) T/4 2/-sixtx). 4 da=dt -0.5 or, ax = dt - 8 sinux -ssinar. As (42)_1 or j 3 He/dt = { // sticht 3 [2 x 1X0.5+2x1x3 3 [ 0.25 +1.5] = 3(1075}= 5.25 sq. units. 3 Ht at - 3 8 22F(F4-1) du Let 5x-1=t dt - Idr 25x 4 - *Este 2 = 4.1Huset = [5*1*3 +4x284) = 7.5 mily Its tan (3x) dx Let Stansx= t.: 5.3 sec 3 xdn = dt dt, or j tudta -1/12 cos? (3x) dx tox { x 1x3 20.1 sq-units cos²x -,15