Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 120 by novrya last updated on 25/Jan/15

Evaluate ∫tan θ dθ

$${Evaluate}\:\int{tan}\:\theta\:{d}\theta \\ $$

Answered by ssahoo last updated on 06/Dec/14

∫tan θ  dθ  =∫((sin θ)/(cos θ))dθ  substituting cos θ=y  −sin θdθ=dy  ∫((sin θ)/(cos θ))dθ=∫− (dy/y)  =−ln ∣y∣+C  =−ln ∣cos θ∣+C

$$\int\mathrm{tan}\:\theta\:\:{d}\theta \\ $$$$=\int\frac{\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta}{d}\theta \\ $$$$\mathrm{substituting}\:\mathrm{cos}\:\theta={y} \\ $$$$−\mathrm{sin}\:\theta{d}\theta={dy} \\ $$$$\int\frac{\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta}{d}\theta=\int−\:\frac{{dy}}{{y}} \\ $$$$=−\mathrm{ln}\:\mid{y}\mid+{C} \\ $$$$=−\mathrm{ln}\:\mid\mathrm{cos}\:\theta\mid+{C} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com