Further Integration (AQA A-Level Mathematics): Quizzes

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Reverse Chain Rule
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What is the Reverse Chain Rule also known as?

Integration by substitution

What type of function is the Reverse Chain Rule used to integrate?

A composite function

What is the first step when using the Reverse Chain Rule?

Identify the inner function

In substitution, if u=g(x)u = g(x), what must you find next?

dudx\frac{du}{dx}

After integrating with respect to uu, what is the final step?

Substitute u=g(x)u = g(x) back

What is ∫2x⋅cos⁡(x2) dx\int 2x \cdot \cos(x^2) \, dx equal to?

sin⁡(x2)+C\sin(x^2) + C

What is ∫(3x2)(x3+1)5 dx\int (3x^2)(x^3 + 1)^5 \, dx equal to?

(x3+1)66+C\frac{(x^3 + 1)^6}{6} + C

What is ∫2xex2 dx\int 2xe^{x^2} \, dx equal to?

ex2+Ce^{x^2} + C

What is ∫cos⁡(3x) dx\int \cos(3x) \, dx equal to?

13sin⁡(3x)+C\frac{1}{3}\sin(3x) + C

When is the Reverse Chain Rule easiest to apply?

When the derivative of the inner function appears

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