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

What is the integration by parts formula?

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

What is the INLATE rule used for?

Deciding which function is uu and dvdv

In INLATE, which type comes before Exponential?

Trigonometric

For ∫x2exdx\int x^2 e^x dx, which should be uu by INLATE?

x2x^2 (algebraic)

After choosing uu, what do you do with it in the setup?

Differentiate it to find dudu

For ∫xe2xdx\int xe^{2x}dx, what is vv after integration?

12e2x\frac{1}{2}e^{2x}

What happens in ∫excos⁡xdx\int e^x \cos x dx after two iterations?

Returns to original integral

When does integration by parts typically not work?

For composite functions

How can you verify your integration by parts answer?

Differentiate the final answer

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