Tag Archives: Surds

Radical Indefinite Integrals

Radical Indefinite Integrals

Radical Indefinite Integrals should be performed after converting its radical or surd notations into index form. $$\displaystyle \sqrt[n]{x^m} = x^{\frac{m}{n}}$$ Practice Questions Question 1 Find \( \displaystyle \int{\sqrt{x}}dx \). \( \begin{aligned} \displaystyle \require{color} \int{\sqrt{x}}dx &= \int{x^{\frac{1}{2}}}dx &\color{red} \text{convert to index form} \\ &= \dfrac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1} + C \\ &= \dfrac{x^{\frac{3}{2}}}{\frac{3}{2}} + C &\color{red} \text{ensure to convert […]

Rationalising Denominators of Multiple Fractions

Rationalising Denominators of Multiple Fractions

Worked Example of Rationalising Denominators Simplify \( \displaystyle\frac{1}{\sqrt{1} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \cdots + \frac{1}{\sqrt{99} + \sqrt{100}} \). \( \begin{aligned} \displaystyle \require{color}&= \frac{1}{\sqrt{1} + \sqrt{2}} \times \frac{\sqrt{1} – \sqrt{2}}{\sqrt{1} – \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} \times \frac{\sqrt{2} – \sqrt{3}}{\sqrt{2} – \sqrt{3}} + \cdots + \frac{1}{\sqrt{99} + \sqrt{100}} \times \frac{\sqrt{99} – \sqrt{100}}{\sqrt{99} – […]