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1)

Area  of the region {(x,y)}ε R2:yx+3,5y(x+9)15 } is equal to


A) 16

B) 43

C) 32

D) 53

Answer:

Option C

Explanation:

Here, {(x,y)}ε R2:yx+3,5y(x+9)15 }

yx+3

    y{x+3,whenx3x3whenx3

or           y2{x+3whenx33xwhenx3

shown as

1422021305_c17.JPG

Also,  5y(x+9)15

(x+9)5y and x6

shown as 

1422021316_m1.JPG

      { (x,y)ϵR2:yx+3,5y(x+9)15}

1422021842_c18.JPG

  Required area

                               = Area of trapezium ABCD - Area of ABE under parabola- Area of CDE under parabola

                         = 12(1+2)(5)34(x+3)dx13(x+3)dx

                  =152[(3x)3232]34[(x+3)3232]13

    =152+23[01]23[80]

=15223163=152183=32