Where k is a positive integer, evaluate: Possibly make a change of variables? Any help? ~Thanks
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Originally Posted by Anonymous1 Where k is a positive integer, evaluate: Possibly make a change of variables? Any help? ~Thanks You can expand it using the Binomial Theorem...
Sorry, wrong answer.
Originally Posted by chengbin Look closer, the answer is 0 no matter what value of k. It can't be zero ever, because is an even function on a symmetric interval, so . Since on , this integral is always strictly positive. Furthermore, the antiderivative is not . The derivative of that function is .
Originally Posted by redsoxfan325 It can't be zero ever, because is an even function on a symmetric interval, so . Since on , this integral is always strictly positive. Furthermore, the antiderivative is not . The derivative of that function is . I realized that after I posted.
I realized that you realized that after I posted.
Originally Posted by Prove It You can expand it using the Binomial Theorem... Really? The whole thing isn't an issue?
Nope. The binomial theorem works with anything.
Originally Posted by Anonymous1 Where k is a positive integer, evaluate: Possibly make a change of variables? Any help? ~Thanks Use the substitution so that . Also note that . So .
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