Selesaikan persamaan integral.... Question from @mayanghejo

September 2018 2 63 Report

Selesaikan persamaan integral
$\int\limits^4_1 { \frac{ x^{2}-x+1 }{ \sqrt{x} } } \, dx$

arikamachroni X√x - √x - 1/√x dx = 2/5 x²√x ₋ 2/3 x√x + 2√x = 2/5 [ 4²√4₋ 1²√1] - 2/3 [4√4 - 1√1] + 2 [√4 - √1]
= 2/5 [32 -1] - 2/3 [8 - 1] + 2[2-1]
= 2/5 . 31 - 2/3 . 7 + 2.1 (x15)
= 186/15 - 70/15 + 30/15
= 156/15 = 10 2/5

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Takamori37 $\displaystyle \int_1^4\frac{x^2-x+1}{\sqrt{x}}\, dx=\int_1^4x\sqrt{x}-\sqrt{x}+\frac{1}{\sqrt{x}}\, dx \\\\ \int_1^4x^{3/2}-x^{1/2}+x^{-1/2}\, dx=\frac{x^{5/2}}{5/2}-\frac{x^{3/2}}{3/2}+\frac{x^{1/2}}{1/2}]_1^4 \\\\ \frac{2}{5}x^{5/2}-\frac{2}{3}x^{3/2}+2x^{1/2}]_1^4 \\\\ \left(\frac{2}{5}(4)^{5/2}-\frac{2}{3}(4)^{3/2}+2(4)^{1/2}\right)-\left(\frac{2}{5}(1)^{5/2}-\frac{2}{3}(1)^{3/2}+2(1)^{1/2}\right) \\\\$

$\displaystyle \frac{2.32}{5}-\frac{2.8}{3}+2.2-\left(\frac{2}{5}-\frac{2}{3}+2\right) \\\\ \frac{64}{5}-\frac{2}{5}-\frac{16}{3}+\frac{2}{3}+4-2 \\\\ \frac{62}{5}-\frac{14}{3}+2 \\\\ \frac{186-70+30}{15} \\\\ \frac{146}{15}$

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