Question

The area (in sq. units) of the region A = {(x,y) ∈ R × R |0 ≤ x ≤ 3, 0 ≤ y ≤ 4, y ≤ x² + 3x} is:
(A) 26/3
(B) 59/6
(C) 53/6
(D) 8

Answer 1

Answer:

A Options is Right Answer

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Answer 2

Area of the given region is 59/6 sq. units

Option B is correct

•A = {(x,y) ∈ R × R |0 ≤ x ≤ 3, 0 ≤ y ≤ 4, y ≤ x² + 3x}

•Boundaries required are

x≥0 => x=0

x≤3 => x=3

y≥0 => y=0

y≤4 => y=4

y ≤ x² + 3x => y = x²+3x

•Hence, after plotting graph we found that,

•Required area =

0->1∫ ydx + 1 >3∫4dx

0->1∫ (x²+3x)dx + 1 ->3∫4dx

0—>1[1/3(x)³ +(3/2)x²] + 1—>3[4x]

1/3(1)³+3/2(1)² +4(3-1)

1/3 + 3/2 + 8.

2/6 + 9/6 + 48/6

59/6 sq units