" How do you solve Indefinite Integrals using U-Substitution? "

Substitution is a hugely powerful technique in integration.

​Though the steps are similar for definite and indefinite integrals, there are two differences, and many of us have trouble keeping them straight. 

This page sorts them out in a convenient table, followed by a side-by-side example : to the right:

• The disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine.
• Used to create mathematical models in order to arrive into an optimal solution.
• In Physics concepts of calculus include motion, electricity, heat, light, harmonics, acoustics, astronomy, and dynamics. In fact, even advanced physics concepts including electromagnetism and Einstein's theory of relativity use calculus.
• In chemistry, calculus can be used to predict functions such as reaction rates and radioactive decay. In biology, it is utilized to formulate rates such as birth and death rates, model biological research, the use of process calculi to represent biological systems has led to the design of different calculi such as brane calculi and κ-calculus. Both have proved to be useful to model different types of biological systems.
• In economics, calculus is used to compute marginal cost and marginal revenue, enabling economists to predict maximum profit in a specific setting.
  

• In addition, it is used to check answers for different mathematical disciplines such as statistics, analytical geometry, and algebra.
  

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