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# Need help with homework problem finding integral

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This is a homework problem. The problem is: find an integral of 2/3 cos(x) * squareroot(sin(x)) dx using the substitution method. Here is my approach, and I don''t know if this is right because this problem is not in the back of the book. u = sin(x) du/dx = cos(x) du = 2/3 cos(x) dx 3/2 du = cos(x) dx so re-writing the problem: 2/3cos(x) * squareroot(u) * du 2/3cos(x) * squareroot(u) * 3/2 cos(x) dx the problem with my thinking at this point is the 2/3cos(x) * 3/2cos(x) doesn''t seem to actually cancel anything does it? If I assume that it does cancel out the cosine then I get: squareroot(u) * dx u ^ 1/2 2/3 u ^ 3/2 2/3 sin(x) ^ 3/2 which becomes -2/3 cos(x) ^ 3/2 I''m a little bit confused about all of this problem, hmm, please help. Thanks.

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2/3 * cos(x) * sqrt(sin(x)) dx =
2/3 * sqrt(sin(x)) * cos(x) * dx

u = sin(x)
du/dx = cos(x)
du = cos(x) * dx

Notice any similarities between the bolded parts?

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Have you looked at the forum FAQ regarding homework?

Anyway, regarding the problem, two things:
1. You can always check the answer of an integral by deriving it.
2. The reasoning looks alright, but you make two mistakes (at least). The first 2/3 comes out of nowhere, and you don''t replace your variables appropriately. To integrate, you need to have only x''s, or only u''s. Play with your equations a little.

Cédric

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muzzafarath is right. Sub sin. then its a simple u^1/2 if you didnt get it.

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oh, doh, stupid mistakes I should have got it the first time. I really was actually stumped though.

About the homework policy I thought it was okay if you posted your attempt, which I did. Besides, my homework does not get graded so cheating on it would not better me in any way.

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This thread is REALLY on the borderline... in fairness, you''ve stated it is a homework problem and have showed some attempt at the work... it''s the responses that concern me. It would have better to simply state that shadow12345 had made an error in his substitution. The onus is then on him to go back and check his work. If he still cannot find the error, then and only then give more details.

I''ll leave this thread open for the time being... but I don''t want to see anyone giving the answer away.

Timkin

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