2023
Mathematics
67ca00ce0c643c71d77dee1f
Determine the area of the region bounded by y = 2x2 + 10 and Y = 4x + 16 .
A.
18
B.
−10/3
C.
44/3
D.
64/3
Correct Answer: 64/3
Explanation
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 = ∫b a [upper function] - [lower function] dx = ∫3 1 4x + 16 − (2x2+10)dx = ∫3 1 − 2x2 + 4x + 6dx = ((−2x3)/3 + (2x2) + 6x)3 1 = ((−2(3)3)/3 + 2(3)2 + 6(3)) − ((−2(−1)3)/3 + 2(−1)2 + 6(−1)) = 18 - (10/3) = 18 + 10/3 = 64/3
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 = ∫b a [upper function] - [lower function] dx = ∫3 1 4x + 16 − (2x2+10)dx = ∫3 1 − 2x2 + 4x + 6dx = ((−2x3)/3 + (2x2) + 6x)3 1 = ((−2(3)3)/3 + 2(3)2 + 6(3)) − ((−2(−1)3)/3 + 2(−1)2 + 6(−1)) = 18 - (10/3) = 18 + 10/3 = 64/3THIS WEEK's
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