tag:blogger.com,1999:blog-2400513859305780710.post7970977250951778133..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: What Can Integrals Do For You? Topic: Calculus.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2400513859305780710.post-67149520480349319262007-01-15T13:12:16.000-08:002007-01-15T13:12:16.000-08:00omg I get this onePractice problem: integration by...omg I get this one<br><br>Practice problem: integration by parts. so u=f(x) dv=derivative of f(x)<br>and u solve.... umm.... <br><br>well, wut about if you take the f(x) out of the integral, then the integral of the derivative would be f(x) so the first whole part is (f(x))^2, and the second part, it's the area of f(x) between 0 and 1, so .. i know starts from the origin, and the area squared... and take half of that, which is probably (f(x)) ^2 times 1/2, so the second whole part is only half of the first blob. <br><br>ok, i know there's gotta be something wrong in that shpeel, but the practice problem has nothing to do with your real problem. i get the arcsin part...Xuanhttp://www.xanga.com/xuannynoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-65718651972385627912007-01-15T14:11:43.000-08:002007-01-15T14:11:43.000-08:00Lol. You can't take f(x) out of the integral. ...Lol. You can't take f(x) out of the integral. But a good substitution for the left side would be u = f(x), du = f'(x)dx.<br><br>And for the right side, think about what you know if f(x) is increasing and try to match it with what you got from the left side.paladin8noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-86329103879839873122007-01-16T10:39:17.000-08:002007-01-16T10:39:17.000-08:00substitution's a good idea haha so the integra...substitution's a good idea haha so the integral becomes 1/2 (int f(x))^2 from 0 to 1 (which is not the same as 1/2 (int f(x) from 0 to 1)^2 of course)<br><br>let int f(x) = F(x), then the LHS is 1/2 F(1)^2 - F(0)^2 whereas the RHS is 1/2 ( F(1) - F(0) )^2, and since f(0) = 0 and f(x) is increasing then -2 F(1) F(0) is nonnegative, so the result is obvioust0rajir0unoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-9882238986084768712007-01-17T09:26:30.000-08:002007-01-17T09:26:30.000-08:00how can you conclude that f(x) is increasing just ...how can you conclude that f(x) is increasing just by the point f(0)=0?Xuanhttp://www.xanga.com/xuannynoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-66638432192783827162007-01-17T09:51:55.000-08:002007-01-17T09:51:55.000-08:00"Let f(x) be a differentiable and increasing ..."Let f(x) be a differentiable and increasing function..."paladin8noreply@blogger.com