April 10, 2024
To find the derivative of \( x\sin x \) we will need to use the product rule. Furthermore, we will also need to recall the derivatives of $x$ and $\sin x$. Specifically, $$\dfrac d{dx} x = 1$$ and $$\dfrac d{dx}\sin x = \cos x$$ If you would like a refresher on how to find the […]
April 9, 2024
In order to find the integral of 1 x 2, we will use the power rule. In other words, we want to use $$ \dfrac d{dx}x^n = nx^{n-1}$$ to find $$\displaystyle\int \dfrac{1}{x^2}dx$$ At first, it is not clear how the two are related. Recall, however, that another name for the integral is antiderivative. In other […]
April 9, 2024
In the realm of calculus, certain integrals stand out for their frequent application and the elegant techniques required for their resolution. One such integral is \( \int \dfrac{1}{x^2+1} dx \), notable for its direct connection to the arctangent function, a fundamental element in trigonometric calculations. The process of integrating \( \dfrac{1}{x^2+1} \) showcases the synergy […]
