Question

4 3 ND 1 7 1 2 3 4 7 To find the blue shaded area above, we would calculate: f(x)dx = area Where: b = f(x) = Area =

Answer 1

The region region R shaded iu figt The line yz f(x) is Porno Ky24x) 7x function passes through (4,0) and (0,4) Its equation is 1 2 figs X-0 1-4 4-0 = 0-4 Y = 4-x and area a aza, the region is from na to x = 2 sfixida, where a 6-2 foo12 (4-x s (A-x) dx 2 Area 2 2 2 ={4x - x2 ] 2 09 کیا اور ان ان افراد Luis X hla ()'

Answer 2

SOLUTION :

            b

Area = ∫  f(x) dx

           a

where, 

a = 1 , b = 2 ,

f(x) = - x + 4  (since slope is - 1, and y-intercept is 4)

So, 

            

Area 

   2

= ∫  (- x + 4) dx 

   1

                             2

=  [- x^2 / 2 + 4x ]

                             1

= [ (- 2^2 / 2 + 4*2) - (- 1^2 / 2 + 4*1)]

= [ 6  - 7/2 ]

= 5 / 2

= 2.5   (ANSWER)

Check :

Graphically , Area = (3 + 2)/2 * 1 = 2.5 (same as above).