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Evaluate the following definite integrals: If ∫0a(2x+1)⋅dx = 2, find the real value of a. - Mathematics and Statistics

Sum

Evaluate the following definite integrals: If `int_0^"a" (2x + 1)*dx` = 2, find the real value of a.

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Solution

Given, `int_0^"a" (2x + 1)*dx` = 2

∴ `[(2x^2)/2 + x]_0^"a"` = 2

∴ `[x^2 + x]_0^"a"` = 2

∴ [(a2 + a) – (0)] = 2
∴ a2 + a = 2
∴ a2 + a – 2 = 0
∴ a2 + 2a – a – 2 = 0
∴ a(a + 2) – 1(a + 2) = 0
∴ (a + )(a – 1) = 0
∴ a + 2 = 0 or a – 1 = 0
∴ a = – 2 or a = 1.

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