Question

Integrate with respect to x :
∫41x+1x√dx

Answer 1

Answer on Question #50932, Math, Integral Calculus

$$\int_{1}^{4} \left(x + \frac{1}{\sqrt{x}}\right) dx$$

Solution.

$$\begin{aligned} & \int_{1}^{4} \left(x + \frac{1}{\sqrt{x}}\right) dx = \int_{1}^{4} x \, dx + \int_{1}^{4} \left. \frac{1}{\sqrt{x}} \right. dx = \left. \frac{x^2}{2} \right|_{1}^{4} + \left. \frac{x^{-\frac{1}{2} + 1}}{-\frac{1}{2} + 1} \right|_{1}^{4} = \\ & = \frac{4^2}{2} - \frac{1^2}{2} + \frac{4^{\frac{1}{2}}}{2} - \frac{1^{\frac{1}{2}}}{2} = 8 - \frac{1}{2} + \frac{2}{\frac{1}{2}} - \frac{1}{\frac{1}{2}} = 8 - \frac{1}{2} + 4 - 2 = 9,5. \end{aligned}$$

Answer: 9,5

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