USEFUL FORMULAS. XXVll 



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P — ^ dx = J V-, Ce -"= ^' dx = i V(7r/a^). 



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Wir. 



P -"'-^^ .V '"dx= I .s-S-.. (2 // -i)a-" (2 ^) -<" + ' 



p-"^ x-i dx = V(Tr/a). 

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IT TT 



I sin wa- sin «ji; ^a- ^ j cos mx cos «:*: ^j; = o. 

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when »i and n are unequal integers. 



/sin ;wa: cos nx dx = — ^ , for ;/'^ and ;z intesrers and m — « odd, 



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= o, for m and « integers and ;;^ — n even. 



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I sin^ mx dx = | cos'^ mx dx = ^ tt, for »^ an integer. 

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^TT ^TT I 



fsin" X dx = fcos" .v dx = C(i — x^^^"-'^^ dx. 



GOO 



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/sin jc , Tcos X ^ .// , X 



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I sin x' dx = i cos .a;^ ^/o: = J 'V (7r/2). 



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p -"' ^^^ COS 2dx dx=\e-^''' "^' V{iT/d). 

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I ^- «'' ^'' sin 2l>x dx=o. 

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