Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 9821 by ridwan balatif last updated on 06/Jan/17

Commented by prakash jain last updated on 08/Jan/17

Is the question  Given f(x)=f(x+2)  and ∫_0 ^2 f(x)dx=B  then find ∫_3 ^7 f(x)dx  ∫_3 ^7 f(x)dx=∫_3 ^5 f(x)dx+∫_5 ^7 f(x)dx  =2∫_3 ^5 f(x)dx  2∫_3 ^5 f(x)dx=2(∫_3 ^4 f(x)dx+∫_4 ^5 f(x)dx)  =2(∫_3 ^4 f(x)dx+∫_2 ^3 f(x)dx)=2∫_2 ^4 f(x)dx=  =2B

$$\mathrm{Is}\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{Given}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right) \\ $$$$\mathrm{and}\:\int_{\mathrm{0}} ^{\mathrm{2}} {f}\left({x}\right){dx}={B} \\ $$$$\mathrm{then}\:\mathrm{find}\:\int_{\mathrm{3}} ^{\mathrm{7}} {f}\left({x}\right){dx} \\ $$$$\int_{\mathrm{3}} ^{\mathrm{7}} {f}\left({x}\right){dx}=\int_{\mathrm{3}} ^{\mathrm{5}} {f}\left({x}\right){dx}+\int_{\mathrm{5}} ^{\mathrm{7}} {f}\left({x}\right){dx} \\ $$$$=\mathrm{2}\int_{\mathrm{3}} ^{\mathrm{5}} {f}\left({x}\right){dx} \\ $$$$\mathrm{2}\int_{\mathrm{3}} ^{\mathrm{5}} {f}\left({x}\right){dx}=\mathrm{2}\left(\int_{\mathrm{3}} ^{\mathrm{4}} {f}\left({x}\right){dx}+\int_{\mathrm{4}} ^{\mathrm{5}} {f}\left({x}\right){dx}\right) \\ $$$$=\mathrm{2}\left(\int_{\mathrm{3}} ^{\mathrm{4}} {f}\left({x}\right){dx}+\int_{\mathrm{2}} ^{\mathrm{3}} {f}\left({x}\right){dx}\right)=\mathrm{2}\int_{\mathrm{2}} ^{\mathrm{4}} {f}\left({x}\right){dx}= \\ $$$$=\mathrm{2}{B} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com