Math Problem Statement

in the integral limit of a to 0 of 4x/9+4x squared dx =1/2ln5 determine the value of a

Solution

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Math Problem Analysis

Mathematical Concepts

Integration
Substitution in Integrals
Logarithmic Functions

Formulas

Substitution: u = 9 + 4x^2
Logarithmic Identity: ln(a) - ln(b) = ln(a/b)
Definite Integral: ∫ du/u = ln|u|

Theorems

Fundamental Theorem of Calculus
Logarithmic Properties

Suitable Grade Level

Undergraduate Calculus