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Determine the area of the region bounded by y = 2x2 + 1...

Determine the area of the region bounded by y = 2x2 + 10 and Y = 4x+16.

A.

18

B.

103

C.

443

D.

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

Open photo
Area = ba [upper function] - [lower function] dx

 

= 314x+16(2x2+10)dx

= 312x2+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