Integration by Parts (Leaving Cert Applied Maths): Quizzes

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Integration by Parts
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What is integration by parts primarily used for?

Integrating products of two functions

Integration by parts is essentially the reverse of which differentiation rule?

The product rule

What is the integration by parts formula?

∫u⋅dv=uv−∫v⋅du\int u \cdot dv = uv - \int v \cdot du

In the INLATE rule, what does the letter 'L' represent?

Logarithmic functions

In the INLATE rule, what does 'A' stand for?

Algebraic functions

According to INLATE, which function should be chosen as uu (to differentiate)?

The one appearing earlier in INLATE

For ∫xe2xdx\int xe^{2x}dx, which should be uu according to INLATE?

xx (algebraic)

What must you do before applying the integration by parts formula?

Differentiate uu and integrate dvdv

What happens in some integration by parts problems like ∫excos⁡xdx\int e^x \cos x dx?

Multiple applications are needed

What should you do if integration by parts leads back to the original integral?

Solve algebraically for the integral

For which type of functions should you consider substitution instead of integration by parts?

Composite functions

How can you verify your integration by parts answer?

Differentiate to get original function

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