The integral is equal to

Engineering

Mathematics

Properties of Definite Integral

Question

The integral $\int_{2}^{4} \frac{{logx}^{2}}{{logx}^{2} + \log (36 - 12 x + x^{2})} dx$ is equal to

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$Let I = \int_{2}^{4} \frac{{ℓogx}^{2}}{{ℓogx}^{2} + ℓog {(x - 6)}^{2}} dx$ ......... (A)

$Also, I = \int_{2}^{4} \frac{\log {(x - 6)}^{2}}{\log {(x - 6)}^{2} + {logx}^{2}} dx$ ......(B) (using king property)

$∴ (A) + (B) \Rightarrow 2 I = \int_{2}^{4} 1 dx \Rightarrow I = \frac{2}{2} = 1 .$