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
= 3∫14x+16−(2x2+10)dx
= 3∫1−2x2+4x+6dx
= (−2x33+2x2+6x)13
= (−2(3)33+2(3)2+6(3))−(−2(−1)33+2(−1)2+6(−1))
= 18 - (103)
= 18 + 103
= 643
