### Integration techniques Part III

Integrating fractions

Revision of anti chain rule

"Increase power by 1 and divide by the new power"

Recall the differentiation of ln (ax + b)

Technique 1: Finding the gradient of a line Parallel lines Parallel lines have the same gradient Perpendicular lines If a line has a gradient of 1/2 , the gradient of the line perpendicular to it is -2. -2 is the negative reciprocal of 1/2. In other words, we "flip" the fraction 1/2 to get 2 and attach a negative sign Technique 2: Finding equation of a straight line The general format of a straight line is y = mx + c where m is the gradient and, c is the y intercept Example 2 Find the equation of a line that contains the points (1,2) and (3,4). From the example above we know that gradient of the line is 1. Hence the equation of the line is: y = 1x + c To find the y intercept, c, we sub in one of the points I choose the point (1,2) and sub x =1, y = 2 2 = 1 + c Hence c = 1 The equation of the line is y = x + 1 Let us combine the techniques we have learnt so far to solve a typical O Level question Question 1 The figure above shows a trapezium where AB is parallel to CD. Both

Integrating fractions: Good explanations. Thanks.

ReplyDeleteThe first one is wrong; it should just be to the power of one in the denominator

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