Finding the Indefinite Integral: A Calculus Homework Question

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SUMMARY

The discussion focuses on solving a calculus problem involving finding the indefinite integral of the expression Inte[(-(x)/((x + 1) - (x + 1)^(1/2))) dx]. Participants also explore a related word puzzle where letters correspond to their positions in the alphabet, aiming to find a word that sums to exactly 100. The method involves summing the values of letters, with a reference to a useful link for further exploration. The problem combines mathematical integration techniques with a creative word challenge.

PREREQUISITES
  • Understanding of indefinite integrals in calculus
  • Familiarity with algebraic manipulation
  • Basic knowledge of letter-to-number correspondence (A=1, B=2, etc.)
  • Experience with online resources for problem-solving
NEXT STEPS
  • Study techniques for solving indefinite integrals, focusing on integration by substitution
  • Explore the concept of letter values in word puzzles and their applications
  • Learn about the properties of definite and indefinite integrals in calculus
  • Investigate online tools and resources for solving complex calculus problems
USEFUL FOR

Students in calculus courses, educators teaching integration techniques, and puzzle enthusiasts interested in word-value challenges.

joxer06
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Hi everyone. I have this problem for my calculas class. So far i can only get a word which adds up to 94. any help is greatly appreciated.

For the alphabet, let a=1, b=2, ... z=26 then, you can start adding up letters of a word. For example, "love" = l+o+v+e = 12+15+22+5 = 54. So, love is 54% important. If you get a word that adds up to more than 100, subtract 100 from it until you get a number equal to or less than 100. The question is: can you find a word that adds up to 100 exactly?
 
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hi
can anyone help me with this exercise
Inte[(-(x)/((x + 1) - (x + 1)^(1/2))) dx]
and the question is: find the indefinite integral

thanks
 
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Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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