RULEMATH | MATH ONLINE/DIRECT CLASS | MATH WEBSITE | SCIENCE CLASS 10, PHYSICS CLASS 11 AND 12

   Hi students,         Are you ready for your Mathematics Board Examination?                                                       Let me first discuss the things that students normally do. Right from the reopening date till date, we are of the opinion that we have a lot of time to prepare for our board exam. We have our own justifications, some of which are as follows: I will forget if I start preparing too early. Only last few months of study will help.  No, a small correction - Only last few weeks of study will help.   Sorry, final correction - Only last few days of study will help. I will practice Math after I complete all other subjects. I will dedicate one full month for Mathematics. I will work 12 - 15 hours a day for Math alone during my study holidays. I will get ready just by doing the sums giv...

 INTEGRALS PART 8 Integration of functions where the numerator as well as the denominator are algebraic functions In such types, apply appropriate algebraic identities and if necessary, split the numerator. In trigonometric functions, use algebraic as well as trigonometric identities to simplify the function and then it can be easily integrated using integral formulae. TRIGONOMETRY INTEGRAL FORMULAE USED IN THE ABOVE SUMS INTEGRAL FORMULAE

 INTEGRALS PART 7 HOW TO INTEGRATE TRIGONOMETRIC FUNCTIONS USING TRIGONOMETRIC IDENTITIES: INTEGRALS USING TRIGONOMETRIC IDENTITIES TRIGONOMETRIC IDENTITIES USED TRIGONOMETRIC IDENTITIES

  INTEGRALS PART 6 HOW TO INTEGRATE BY RATIONALISING THE DENOMINATOR: Rationalize the denominator  First of all, rationalize the denominator by multiplying both the numerator and denominator with the conjugate.  Apply algebraic identity and simplify the function. Apply integral formula.

  INTEGRAL NOTES PART 5 HOW TO INTEGRATE  INTEGRALS OF THE FOLLOWING TYPES: Add and subtract so as to get like terms and then split the integrals. Use laws of exponents and apply integral formula.

  INTEGRALS PART 9 HOW TO INTEGRATE  ALGEBRAIC FUNCTIONS  OF HIGHER POWERS Such types of integrals can be easily done through Substitution method.  ALGEBRAIC FUNCTIONS In the case of trigonometric functions like the one below, multiply the numerator and denominator with a suitable trigonometric ratio. Make a proper substitution so that the function and the differential is satisfied. Apply integral formula. TRIGONOMETRIC FUNCTIONS

  INTEGRALS PART 10 HOW TO PROVE  FORMULA FOR INTEGRALS  BASED ON EXPONENTIAL FUNCTIONS EXPONENTIAL  FUNCTIONS EXAMPLE EXAMPLE OF INTEGRALS BASED ON EXPONENTIAL FUNCTIONS SPECIAL TYPE OF EXPONENTIAL INTEGRALS EXAMPLE OF A SPECIAL TYPE OF EXPONENTIAL INTEGRALS