Integration of Trigonometric Functions - Practice Questions & MCQ

Trigonometric Functions

1. $\frac{d}{d x}(-\cos x)=\sin x \Rightarrow \int \sin x d x=-\cos x+C$
2. $\frac{d}{d x}(\sin \mathrm{x})=\cos \mathrm{x} \Rightarrow \int \cos \mathrm{xdx}=\sin \mathrm{x}+\mathrm{C}$
3. $\frac{\mathrm{d}}{\mathrm{dx}}(\tan \mathrm{x})=\sec ^2 \mathrm{x} \Rightarrow \int \sec ^2 \mathrm{xdx}=\tan \mathrm{x}+\mathrm{C}$
4. $\frac{\mathrm{d}}{\mathrm{dx}}(-\cot \mathrm{x})=\csc ^2 \mathrm{x} \Rightarrow \int \csc ^2 \mathrm{xdx}=-\cot \mathrm{x}+\mathrm{C}$
5. $\frac{d}{d x}(\sec x)=\sec x \tan x \Rightarrow \int \sec x \tan x d x=\sec x+C$
6. $\frac{d}{d x}(-\csc x)=\csc x \cot x \Rightarrow \int \csc x \cot x d x=-\csc x+C$

Integrals of tan x, cot x, sec x, cosec x

7. $\frac{\mathrm{d}}{\mathrm{dx}}(\log |\sin \mathrm{x}|)=\cot \mathrm{x} \Rightarrow \int \cot \mathrm{xdx}=\log |\sin \mathrm{x}|+C$
8. $\frac{d}{d x}(-\log |\cos \mathrm{x}|)=\tan \mathrm{x} \Rightarrow \int \tan \mathrm{xdx}=-\log |\cos \mathrm{x}|+\mathrm{C}$
9. $\frac{d}{d x}(\log |\sec \mathrm{x}+\tan \mathrm{x}|)=\sec \mathrm{x} \Rightarrow \int \sec \mathrm{xdx}=\log |\sec \mathrm{x}+\tan \mathrm{x}|+C$
10. $\frac{\mathrm{d}}{\mathrm{dx}}(\log |\csc \mathrm{x}-\cot \mathrm{x}|)=\csc \mathrm{x} \Rightarrow \int \csc \mathrm{xdx}=\log |\csc \mathrm{x}-\cot \mathrm{x}|+\mathrm{C}$