Question and Answers Forum

All Questions      Topic List

UNKNOWN Questions

Previous in All Question      Next in All Question      

Previous in UNKNOWN      Next in UNKNOWN      

Question Number 30354 by soksan last updated on 21/Feb/18

$$\mathrm{If}g\left(x\right)={\stackrel{x}{\int }}_0{\cos }^{4}tdt,\mathrm{then}g(x+\pi )=$$

Answered by ajfour last updated on 21/Feb/18

$$g\left(x\right)=\frac{1}{4}{\int }_0^x{\left(2\cos {}^{2}t\right)}^{2}dt$$$$=\frac{1}{4}{\int }_0^x{(1+\cos 2t)}^{2}dt$$$$=\frac{1}{4}{\int }_0^x(1+2\cos 2t+\cos {}^{2}2t)dt$$$$=\frac{x}{4}+\frac{\sin 2x}{4}+\frac{1}{8}{\int }_0^x(1+\cos 4t)dt$$$$=\frac{x}{4}+\frac{\sin 2x}{4}+\frac{x}{8}+\frac{\sin 4x}{32}$$$$g(x+\pi )=g\left(x\right)+\frac{3\pi }{8}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com