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Edexcel A-level Maths Basics of integration

Basics of integration

This page covers the following topics:

The Fundamental Theorem of Calculus states that integration is the inverse process of differentiation. During differentiation, the constant terms of the function being differentiated will disappear. Thus, to account for this in integration, a constant is added to the integral. This constant is usually expressed as c and is called the constant of integration.

Fundamental theorem of calculus

The integral of a polynomial ax^n is given by ax^(n + 1)/(n + 1) + c, where c is the constant of integration.

Integrating polynomials

During differentiation, the constant terms of the function being differentiated will disappear. Thus, to account for this in integration, a constant is added to the integral. This constant is usually expressed as c and is called the constant of integration.

Constant of integration

Indefinite integrals do not have an evaluated constant of integration. They represent a family of functions which have the same derivative, and their only difference is the value of the constant of integration.

Indefinite integrals

1

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Demonstrate the Fundamental Theorem of Calculus using the following equation: y = 10sinx + 6x + 10.

Edexcel A-level Maths Basics of integration Demonstrate the Fundamental Theorem of Calculus using the following equation: y = 10sinx + 6x + 10.
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2

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A function is differentiated and then integrated. What is the result?

Edexcel A-level Maths Basics of integration A function is differentiated and then integrated. What is the result?
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3

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Integrate y = 10.

Edexcel A-level Maths Basics of integration Integrate y = 10.
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4

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Given that the constant of integration is 5, find the integral of 5x⁴ + 27x².

Edexcel A-level Maths Basics of integration Given that the constant of integration is 5, find the integral of 5x⁴ + 27x².
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5

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What is the function of the velocity of the object whose acceleration is given by a = 20t + 50, where t is time in seconds?

Edexcel A-level Maths Basics of integration What is the function of the velocity of the object whose acceleration is given by a = 20t + 50, where t is time in seconds?
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6

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Evaluate ∫10x + 8dx.

Edexcel A-level Maths Basics of integration Evaluate ∫10x + 8dx.
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7

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Given that the constant of integration is βˆ’4, evaluate ∫5x⁴ + 20xdx.

Edexcel A-level Maths Basics of integration Given that the constant of integration is βˆ’4, evaluate ∫5x⁴ + 20xdx.
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8

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Given that the gradient of the graph is given by dy/dx = 10x + 10 and that at x = βˆ’1, y = βˆ’9, find the equation of the graph.

Edexcel A-level Maths Basics of integration Given that the gradient of the graph is given by dy/dx = 10x + 10 and that at x = βˆ’1, y = βˆ’9, find the equation of the graph.
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9

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Solve the integral ∫4x + 32x⁷dx.

Edexcel A-level Maths Basics of integration Solve the integral ∫4x + 32x⁷dx.
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10

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Two functions are found to have the same indefinite integral. Explain what this means.

Edexcel A-level Maths Basics of integration Two functions are found to have the same indefinite integral. Explain what this means.
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