u-Substitution

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What is u-substitution in integration?

Back

U-substitution is a method used to simplify the process of integration by substituting a part of the integrand with a new variable (u), making the integral easier to solve.

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How do you choose u in u-substitution?

Back

Choose u to be a function inside the integral that simplifies the expression when differentiated. Common choices include polynomials or expressions that are raised to a power.

Front

What is the derivative of u with respect to x in u-substitution?

Back

If u = g(x), then the derivative is du/dx = g'(x). This relationship is used to replace dx in the integral.

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What is the formula for u-substitution?

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Front

What is the purpose of the constant C in integration?

Back

The constant C represents the family of antiderivatives, as indefinite integrals can differ by a constant.

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What is the relationship between definite and indefinite integrals?

Back

Definite integrals compute the area under a curve between two limits, while indefinite integrals represent a family of functions without specific limits.

Front

What is the chain rule in differentiation?

Back

The chain rule states that if a function y = f(g(x)), then the derivative is dy/dx = f'(g(x)) * g'(x). This is essential in u-substitution.