Quiz on Integration Formulae from NCERT Leave a Comment / By Ankur Negi / 4 August 2025 Take the following test to check your knowledge of Integration formulae All the formulae are from NCERT Welcome to your Integration Formulae NCERT1. $$ \int \cos x \ dx = $$ - \sin x + C \sin x + C \tan x +C None 2. $$ \int \sec x \tan x \ dx = $$ \sec x + C \tan x + C \tan ^2 x + C None 3. $$ \int \frac{dx}{\sqrt{1 - x^2}} = $$ - \sin ^{-1} + C \sin^{-1} x + C \cos^{-1} x + C None 4. $$\int a^x \ dx = $$ a^x +C \ a^x \cdot \log a + C \frac{a^x}{\log a} + C None 5. $$ \int \cot x \ dx = $$ - \log |\sin x| + C - \log |\cos x| + C \log |\sin x| + C None 6. $$ \int \frac{dx}{x^2 + a^2} = $$ \frac{1}{2a} \log \left| \frac{x - a}{x + a} \right| + C \frac{1}{a} \tan^{-1} \frac{x}{a} + C \frac{1}{2a} \log \left| \frac{x + a}{x - a} \right| + C None 7. $$ \int \frac{dx}{\sqrt{x^2 - a^2}} = $$ \frac{1}{a} \sin^{-1} \frac{x}{a} + C \sin^{-1} \frac{x}{a} + C \log \left| x + \sqrt{x^2 - a^2} \right| + C None 8. $$ \int e^x \left[ f(x) + f'(x) \right] \ dx = $$ e^x f'(x) + C e^x + f(x) + C e^x f(x) + C None 9. $$ \int \sqrt{a^2 - x^2} \ dx = $$ \frac{1}{2} x \sqrt{a^2 - x^2} + \frac{a^2}{2} \sin^{-1} \frac{x}{a} + C ] \frac{x}{2} \sqrt{a^2 - x^2} - \frac{a^2}{2} \log \left| x + \sqrt{a^2 - x^2} \right| + C \frac{x}{2} \sqrt{a^2 + x^2} - \frac{a^2}{2} \log \left| x + \sqrt{a^2 + x^2} \right| + C None 10. $$ \int \frac{dx}{\sqrt{x^2 + a^2}} = $$ \log \left| x + \sqrt{x^2 + a^2} \right| + C \log \left| x - \sqrt{x^2 - a^2} \right| + C \frac{1}{a} \cdot \tan^{-1}\frac {x}{a} + C None Time's up
