Question

integrate (1-x) √x dx​

Answer 1

(1- x) √x

√x - x³/²

now taking integrate = x³/²×2/3 - x ki power 5/2. ×2/5

Answer 2

Given : $I = \int (1-x)\sqrt{x}dx$

Step-by-step explanation:

$I = \int (1-x)\sqrt{x}dx\\\\solving \\\\= \int (\sqrt{x}-x\sqrt{x})dx\\\\=\int (x^\frac{1}{2}-x^\frac{3}{2})dx\\\\\text{integrating we get}\\\\\frac{x^\frac{1}{2}^+^1}{\frac{1}{2}+1}-\frac{x^\frac{3}{2}^+^1}{\frac{3}{2}+1}+C$

solving

$\frac{2}{3}x^\frac{1}{2}\times x -\frac{2}{5}x^2\times x^\frac{1}{2}+C\\\\= \frac{2}{3}x\sqrt{x}\\\\-\frac{2}{5}x^2\sqrt{x}+c$

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