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I'd say this is a basic integration question checking the basics
Refer to any book on definite integration, you'll find a property that definite integration of any f(x) from 0 to a equals integration of f(a-x) from 0 to a
So first write I as the required integral and then use the above property to rewrite I
Then add both the equstions and you'll see that 2I=x]0 to pi/2 becos f(x) + f(a-x)=1 here ( this is a whole class of questions)
so answer is pi/4
WHy you couldnt do it may be cos you are accustommed more to using indefinite and coulsnt get into the definite system which is simpification first
Cheers
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