Indefinite integrals and substitution (HSC SSCE Mathematics Extension 1): Flashcards
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What is an indefinite integral?
What is an indefinite integral?
An antiderivative without specific limits, includes C.
What does the integral sign represent?
What does the integral sign represent?
It represents the process of integration.
What is the purpose of the substitution method?
What is the purpose of the substitution method?
To simplify difficult integrals by changing variables.
What is the formula for an indefinite integral?
What is the formula for an indefinite integral?
∫f(x)dx = F(x) + C, where F' = f.
How do you apply substitution in integration?
How do you apply substitution in integration?
Choose u=g(x), then rewrite the integral in terms of u.
What is ∫√(4x + 1)dx using substitution?
What is ∫√(4x + 1)dx using substitution?
Result is (1/6)(4x + 1)^(3/2) + C.
What is the solution for ∫x(x^2 + 1)dx?
What is the solution for ∫x(x^2 + 1)dx?
1/2(x^2 + 1)^2 + C using u = x^2 + 1.
What substitution is used for ∫1/(2x√(4-x^2))dx?
What substitution is used for ∫1/(2x√(4-x^2))dx?
Use x = 2sin(θ) for trigonometric substitution.
What is the integral of cos²(x) dx?
What is the integral of cos²(x) dx?
x/2 + (sin(2x)/4) + C using the identity.
What are practical applications of indefinite integrals?
What are practical applications of indefinite integrals?
Used in biology, engineering, and physics for growth.