iPad 10:56 PM 69% socrates.wartburg.edu MA 252 Group Homework 5 Due: 11/09 1. It
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iPad 10:56 PM 69% socrates.wartburg.edu MA 252 Group Homework 5 Due: 11/09 1. It is a beautiful Fall day. You leave your Calculus class with a tingling feeling that fills your toes with boisterous energy. You have just learned about integration by parts and want to shout to the world about it. As you turn a corner, you run into a wild eyed stranger who is watching you malevolently. "Good morning, there." he says. "You look like you just learned integration by parts. Well don't be fooled! It's nothing but lies! Lies!" "Calculus is based on sound logic and proof you retort "Really? Then explain this!" he cries as he scrawls the following on a piece of paper tan(z) dz = / sin(x) sec(z) dz du = sin(r) dr u = sec(x) sec(z) tan(2) dr du -cos(z) u tan(r) dr = uv-1 u du tan(z) dz =-1 + tan(r) dr "Hey," you say, "Zero doesn't equal negative one! I don't get it! No it doesn't! Where's your sound logic and proof now?", he says with a hungry look in his eye Is it true that all of Calculus is based on faulty principles? Or did the wild eyed stranger make a mistake in his computation? Find the error in his reasoning 2. The wild eyed stranger, not satisfied with the confused look on your face, says, "Integration by parts definitely has some serious problems.He snatches the piece of paper out of your hand and writes the following tan(z) dz = sin(x) sec(z) dz = sec(x) du = sin(x) dr du = sec(z) tan(2) dr u=-cos(x) tan(r) duv u du tan(x) dr =-1 + tan(2) dr "Wait! That's not right either." you lament "Ho ho ho! Hee hee hee! cackles the wild eyed stranger with mad glee. And he dashes off around the corner. You are left feeling shaken to the core. Has he managed to destroy the foundations of mathematics? Or can you find the error in this argument?Explanation / Answer
The part where he assumed, dv = sinx dx
dx is not a multiplication factor, It just tells us the variable with respect to which we have to integrate.
furthermore, we can only assume u and v in such a way that their product results....(sinx)(secx) which is what we are integrating.
Here, uv = (secx)(-cosx) = -1 which is absolutely wrong.
Seems that wild eyed stranger doesn't know how to apply By parts.
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