Question

Find the value of ‘a’ if `int_2^a (x + 1)dx = 7/2`

Answer 1

`int_2^a (x + 1)dx = 7/2`

∴ `[x^2/2 + x]_2^a = 7/2`

∴ `(a^2/2 + a) - (4/2 + 2) = 7/2`

∴ `a^2/2 + a - 8/2 = 7/2`

∴ a² + 2a = 15

∴ a² + 2a – 15 = 0

∴ (a + 5)(a – 3) = 0

∴ a + 5 = 0 or a – 3 = 0

∴ a = –5 or a = 3