Class XII Math Preparation Tips and tricks For Integration – How to prepare for board exams?

Class XII Math Preparation Tips and tricks For Integration – How to prepare for board exams?

Many difficult integration issues is resolved astonishingly quickly by merely knowing the correct technique to use.

While finding the correct technique is a matter of ingenuity, there are a dozen or so techniques that permit a more comprehensive approach to solving definite integrals

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Manipulations of definite integrals may rely upon specific limits for the integral, like with odd and even functions, or they may require directly changing the integrand itself, through some type of substitution.

However, most integrals need a mixture of techniques, and many of the more complicated approaches, like interpretation as a double integral, require multiple steps to reduce the expression.

Integration by parts provides a way to change the integrand directly, and like the exploration of inverse functions, it is a geometric statement. However, this is a statement about the geometry of calculus operators, and any visualization of it would lie in an entirely different space. However, the same intuition can apply. Integration by parts is a very powerful tool, and many problems on this page could be solved by this (and more elementary methods) without the need for anything more complicated.

Pdf download for all tricks to solve the problem and all forms of integrals

Integration by parts states that for any differentiable functions u(x)u(x) and v(x)v(x), the following equivalence holds in pdf.

Let us take up consecutive topic Integration (Chapter 7), which is a big chapter.

You may recall that the full Calculus has forty four marks.

Out of that nineteen marks ar assigned to chapters seven and eight (Integration and its application).

Normally 12-13 marks are allotted to chapter 7.

You should positively expect 3 4-mark queries during this topic.

In most cases, you’ll find two 4-mark question from Indefinite integration and one 4-mark question from Definite integral.

Tip: Please bear in mind that this chapter has several formulae however the patterns of queries ar fastened.

Normally no tricky question is expected here. Just practise all the patterns carefully and be careful about the calculations in Ex 7.5 (partial fraction).

You can use the choice technique to ascertain the values of the constants.

In this Chapter

Pdf download for all tricks to solve the problem and all forms of integrals

1. The General Power Formula

2. The Basic Logarithmic Form

3. The Exponential Form

4. The Basic Trigonometric Forms

5. Other Trigonometric Forms

6. Inverse Trigonometric Forms

7. Integration by Parts

8. Integration by Trigonometric Substitution

9. Integration by Use of Tables

Table of Common Integrals

10. Integration by Reduction Formulae

11. Integration by Partial Fractions

Tips:

.Remember standard Formulae

.Knowing the nature of the functions

.Use graphs whenever possible

..Integration

.Keep Practising

Suggested video:

https://youtu.be/MW_tl_8wd-c

https://youtu.be/MW_tl_8wd-c

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Pdf download for all tricks to solve the problem and all forms of integrals

Download all formulas