Question

Esboce a região cuja área é representada pela integral definida e calcule tal integral.

Answer 1

$\displaystyle \int\limits^4_1 \frac{4\text{dx}}{\sqrt{\text x}} \to\ 4\int\limits^4_1\frac{\text {dx}}{\sqrt{\text x}} \\\\\\ 4\int\limits^4_1 \text x^{(\displaystyle\frac{-1}{2})}\text{dx} \\\\\\ 4\left[\begin{array}{c} \frac{\displaystyle \text x^{\displaystyle (\frac{-1}{2}+1)}}{\displaystyle \frac{-1}{2}+1}\end{array}\right]\limits^4_1 \\\\\\4\left[\begin{array}{c} 2.\sqrt{\text x}\end{array}\right]\limits^4_1 \\\\\\ 4.2.[\ \sqrt{4}-\sqrt{1}\ ] \\\\ 4.2.[2-1] \\\\ 8$

$\displaystyle \underline{\text{Portanto}}: \\\\\\ \huge\boxed{\int\limits^4_1 \frac{4}{\sqrt{\text x}}\text{dx} = 8 \ }\checkmark$