1-a-4-x-k-x-1-4a-3-Find-the-value-of-1-a-1-x-1-dx-

Question Number 129269 by bramlexs22 last updated on 14/Jan/21

\int_{1}^{a} \frac{4 \sqrt{x} + k}{\sqrt{x} + 1} = 4 a + 3 . Find the value

of \int_{1}^{a} \frac{1}{\sqrt{x} + 1} d x .

Answered by liberty last updated on 14/Jan/21

\int_{1}^{a} \frac{4 \sqrt{x} + 4 + k - 4}{\sqrt{x} + 1} d x = 4 a + 3

\int_{1}^{a} 4 d x + (k - 4) \int_{1}^{a} \frac{d x}{\sqrt{x} + 1} = 4 a + 3

4 a - 4 + (k - 4) \int_{1}^{a} \frac{d x}{\sqrt{x} + 1} = 4 a + 3

\Rightarrow \int_{1}^{a} \frac{d x}{\sqrt{x} + 1} = \frac{7}{k - 4}

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