Let’s try some calculus questions

Many students often overlook that the coefficient of $x$ in the integration or differentiation formulas in MF15 is 1!!! When it is not 1, many things changes. I’ll let the examples do the talking. 🙂

Differentiation (recall chain rule)

$\frac {d}{dx}(sin^{-1}(3x^2)) = \frac {1}{\sqrt{1-(3x^2)^2}}(6x)$

Integration

$\int \frac {1}{4+9x^2} dx = \frac {1}{2} {tan^{-1}(\frac {3x}{2})}\times\frac{1}{3}$

For my careless students, I usually recommend they make the case of the coefficient of $x$ be ONE instead. So $\int \frac {1}{4+9x^2} dx = \frac{1}{9}\int \frac {1}{\frac{4}{9}+x^2} dx$ and after applying formula gives, $(\frac{1}{9})(\frac{1}{\frac{2}{3}}){tan^{-1}(\frac {x}{\frac{2}{3}})}$ which will give the same answers after simplifications.

Practice

You may practice a few of the following questions!

$\int\frac {1}{4-9x^2}dx$

$\int\frac {1}{9x^{2}-4}dx$

$\int\frac {1}{\sqrt{4-9x^2}}dx$

$\int\frac {1}{2x^{2}-2x-10}dx$

Let me know if you have problems!

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

Let’s try some calculus questions

Differentiation (recall chain rule)

Integration

Practice

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