Determine the area of the region bounded by y = 2x2 + 10 and Y = 4x+16.
18
−103
443
643
Correct answer is D
To find the point of intersection, equate the two equations
⇒ 2x2 + 10 = 4x + 16
⇒ 2x2 + 10 - 4x - 16 = 0
⇒ 2x2 - 4x - 6 = 0
Factorize
⇒ 2(x + 1)(x - 3) = 0
∴ x = -1 or 3
The curves will intersect at -1 and 3
Area = ∫ba [upper function] - [lower function] dx
= ∫314x+16−(2x2+10)dx
= ∫31−2x2+4x+6dx
= (−2x33+2x2+6x)31
= (−2(3)33+2(3)2+6(3))−(−2(−1)33+2(−1)2+6(−1))
= 18 - (103)
= 18 + 103
= 643
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