If ∫0a(2x+1) dx = 2, find a - Mathematics and Statistics

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Sum

If `int_0^"a" (2x + 1)  "d"x` = 2, find a

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Solution

Given, `int_0^"a" (2x + 1)  "d"x` = 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 + 2)(a – 1) = 0 

∴ a + 2 = 0 or a – 1 = 0

∴ a = – 2 or a = 1

Concept: Fundamental Theorem of Integral Calculus
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Chapter 1.6: Definite Integration - Q.4

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