1. Show that for sinx+cos x dx = /2 sin x T 2. The German mathematician...

 

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1. Show that for sin²x+cos² x dx = π/2 sin² x T 2. The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t = tan will convert any rational function of sin x and cos x into an ordinary rational function of t. It can be shown that COS X = Cπ/2 1-t² 1+t2: Show that f sin x = 2t 1+t2, and dx = 2 1+t² dt. dx = by making the above substitutions (remembering to also convert the interval of integration) and using techniques of integration discussed this semester. sin x sin x+cos x 1. Show that for sin²x+cos² x dx = π/2 sin² x T 2. The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t = tan will convert any rational function of sin x and cos x into an ordinary rational function of t. It can be shown that COS X = Cπ/2 1-t² 1+t2: Show that f sin x = 2t 1+t2, and dx = 2 1+t² dt. dx = by making the above substitutions (remembering to also convert the interval of integration) and using techniques of integration discussed this semester. sin x sin x+cos x