Question

Tumeumit: 2 hours. 1 To find the blue shaded area above, we would calculate: 1 f(x) dx = area Ja Where: a= = f(x)= Preview Area = Preview

Answer 1

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Hen Equation of the line or function (1,4) and (3, 2). (4-4) = 2-4 (x-1) 3-1 (9-4) = -2 (2-1) = -1 (2-1) 2 y = -2 +2 +4 = -x + 5 - fx) = -x + 5 then from the diagram 9 and b -3 fx = -x + 5 3 Area = (-x+5) dx - + SX (x+5) dx = [- +52] - [4 + 15+ -5) =: 10-4 = 6 CA

Answer 2

SOLUTION :

            b

Area = ∫  f(x) dx

           a

where, 

a = 1 , b = 3 ,

f(x) = - x + 5  (since slope is - 1, and y-intercept is 5)

So, 

            

Area 

   3

= ∫  (- x + 5) dx 

   1

                             3

=  [- x^2 / 2 + 5x ]

                             1

= [ (- 3^2 / 2 + 5*3) - (- 1^2 / 2 + 5*1)]

= [ 21/2  - 9/2 ]

= 12 / 2 

= 6   (ANSWER)

Check :

Graphically , Area = (4 + 2)/2 * 2 = 6 (same as above).