Integration

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Introduction

The gradient function is a formula for the gradient at any point on the curve.

The process of finding the original function f(x); when you know dy/dx (or f '(x) is called integration.

We have to integrate the dy/dx function a term at a time.

Always put +c on the end of the equation.

Add one to the power and divide by the new power.

In general if dy/dx = x^n then y = x^n+1/n+1 +c

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Definite integrals

After you have integrated the function- put both the limits in and find the values.

The subtract what the bottom limit gave you from what the top limit gave you.

Put the integrated function in square brackets and rewrite the limits on the right-hand side.

You don't need a constant of integration with a definite integral.

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Trapezium rule

The trapezium rule is used to find the approximate area under a curve

The area of each trapezium is A = h/2 (yn + yn+1)

The area represented by (integral sign with limits b and a of y dx) is approximately h/2 [y0 + 2(y1+y2+...+yn-1)+yn] where n