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Question
If `int_1^"a" (3x^2 + 2x + 1) "d"x` = 11, find the real value of a
Solution
Given, `int_1^"a" (3x^2 + 2x + 1) "d"x` = 11
∴ `[(3x^3)/3 + (2x^2)/2 + x]_1^"a"` = 11
∴ `[x^3 + x^2 + x]_1^"a"` = 11
∴ (a3 + a2 + a) – (1 + 1 + 1) = 11
∴ a3 + a2 + a – 3 = 11
∴ a3 + a2 + a – 14 = 0
∴ (a – 2)(a2 + 3a + 7) = 0
∴ a = 2 or a2 + 3a + 7 = 0
But, a2 + 3a + 7 = 0 does not have real roots.
∴ a = 2
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