Integration by substitution (HSC SSCE Mathematics Extension 2): Flashcards
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What is integration by substitution?
What is integration by substitution?
A method to simplify integrals by changing variables.
What does the chain rule relate to in integration?
What does the chain rule relate to in integration?
It inspires the method of integration by substitution.
What is the first step in integration by substitution?
What is the first step in integration by substitution?
Choose a substitution u = g(x).
How do you find du in substitution?
How do you find du in substitution?
Differentiate u = g(x) to get du.
What is the formula for substitution in integrals?
What is the formula for substitution in integrals?
∫ f(g(x))g'(x) dx = ∫ f(u) du.
What is a common mistake in substitution?
What is a common mistake in substitution?
Forgetting to adjust the differential dx.
What is a good strategy for choosing u in integration?
What is a good strategy for choosing u in integration?
Select u as the most complex function to simplify integration.
What is reverse substitution?
What is reverse substitution?
Replacing u with g(x) after solving the integral.
What is a practice problem for substitution?
What is a practice problem for substitution?
Evaluate ∫ x √(x² + 1) dx using substitution.
What is a complex example of substitution?
What is a complex example of substitution?
∫ e^(3x)/√(e^(6x) + 1) dx using u = e^(3x).