@?methods-in-calculus

See Also [[Further Maths - Mean Value of a Function]]S [[Further Maths - Improper Integrals]]S [[Further Maths - Hyperbolic Functions]]S Flashcards $$\frac{d}{dx}(\sin^{-1}(x))$$ What is this equal to?? $$ \frac{1}{\sqrt{1 - x^2}} $$ $$\frac{d}{dx}(\cos^{-1}(x))$$ What is this equal to?? $$ -\frac{1}{\sqrt{1 - x^2}} $$ $$\frac{d}{dx}(\tan^{-1}(x))$$ What is this equal to?? $$ \frac{1}{1 + x^2} $$ $$\int \frac{1}{\sqrt{1-x^2}} dx$$ What is this equal to?? $$ \sin^{-1}(x) + c $$

See Also [[Maths - Integration]]S [[Maths - Integration by Substitution]]S Flashcards What two things mean an integral is improper?? One or both of its limits are infinite It is undefined anywhere in $[a, b]$. What do you call an improper integral that exists (has a defined value)?? Convergent. What do you call an improper integral that does not exist?? Divergent. $$\int^\inft_0 e^{-x} dx$$ What would you write instead to see if it has a defined value?

See Also [[Maths - Integration]]S [[Maths - Integration by Substitution]]S Flashcards What do you divide the definite integral between $[a,b]$ in order to find the mean value?? $$ b - a $$ Backlinks [[Further Maths - Integrating and Differentiating Inverse Trig Functions]]S [[Further Maths - Syllabus]]S Metadata date: 2021-04-27 16:20 tags: - '@?further-maths' - '@?school' - '@?public' - '@?methods-in-calculus' title: Further Maths - Mean Value of a Function