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AQA A-level Maths Methods of integration

Methods of integration

This page covers the following topics:

Integration by parts is a special emthod of integration which is used when two functions are being multiplied. They are defined as u and v accordingly, and the given formula is used to evaluate the interval.

Integration by parts

Integration by substitution is a method to evaluate integrals by changing the variables. This method can be used when the integral is of the given form.

Integration by substitution

When the integrand is in the form of a proper fraction, the integral should be rewritten as partial fractions and then integrated using the given result.

Integrating partial fractions

1

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Use integration by parts to evaluate ∫x(1 + cosx)dx.

AQA A-level Maths Methods of integration Use integration by parts to evaluate ∫x(1 + cosx)dx.
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2

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Without expanding, evaluate ∫xΒ³(x βˆ’ 10) dx.

AQA A-level Maths Methods of integration Without expanding, evaluate ∫xΒ³(x βˆ’ 10) dx.
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3

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Integrate ∫2xcos(x²)dx.

AQA A-level Maths Methods of integration Integrate ∫2xcos(x²)dx.
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4

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Use integration by substitution to find ∫5x⁴cos(x⁡)dx.

AQA A-level Maths Methods of integration Use integration by substitution to find ∫5x⁴cos(x⁡)dx.
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5

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Evaluate ∫20sin(4x) dx.

AQA A-level Maths Methods of integration Evaluate ∫20sin(4x) dx.
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6

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Solve the following integral: ∫5x⁴/(x⁡ + 10)dx.

AQA A-level Maths Methods of integration Solve the following integral: ∫5x⁴/(x⁡ + 10)dx.
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7

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Determine the following integral: ∫(3x + 10)/(2x + 1)²dx.

AQA A-level Maths Methods of integration Determine the following integral: ∫(3x + 10)/(2x + 1)²dx.
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8

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Integrate ∫(24 + 4x)/(x βˆ’ 4)(x βˆ’ 3)dx using partial fractions.

AQA A-level Maths Methods of integration Integrate ∫(24 + 4x)/(x βˆ’ 4)(x βˆ’ 3)dx using partial fractions.
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