Reverse Chain Rule (Edexcel 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

When is the Reverse Chain Rule used?

For composite functions

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

Identify the inner function

After letting u=g(x)u = g(x), what should you find next?

dudx\frac{du}{dx}

What is the final step after integrating with respect to uu?

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

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

sin⁡(x2)+C\sin(x^2) + C

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

ex2+Ce^{x^2} + C

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

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

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

13sin⁡(3x)+C\frac{1}{3}\sin(3x) + C

For ∫2xex2 dx\int 2xe^{x^2} \, dx, what is the inner function?

x2x^2

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