integration

What Happens When Integration Question Is in the form of Product?

I posted an interesting question on Integration here.

Allow me to repeat. There isn’t any product rule nor quotient rule in Integration.

So to Integrate the question, some "extra" work must be done to "dissolve" the product nature of the question.

These are the steps that must be taken even before Integration beings:

Factorise the terms inside the Square Root
Combine common term (2x+1) by applying Indices Law
Remember to + c as this is a indefinite integral aka no limits given

Integration Mixed With Differentiation

In Integration, unlike Differentiation, there isn't any product rule nor quotient rule. Having said this, examiners always like to present question in that form of either product or quotient. Students who aren't able to see through their plot to confuse your mind will fall straight into their trap.
So LOOK OUT!

The question most students will ask next will be what to do when the Integration is presented in the manner as if we can use product or quotient rule aka the given question is in the form of a fraction.

These are the few ways you can work around it

Simplifying either by breaking up the numerator
Simplification by applying Indices Law (very useful when you are working with exponential or bases-powers)
Apply partial fraction concept

Look at this question:
$\int (2x+1)\sqrt{8x+4} dx$

It is expressed as two product. How do we integrate?

Discuss your approach in the comment box below.

I will reveal the step by step approach by end of this week. Be sure to subscribe to www.singaporeolevelmaths.com/feed so that you will be notified of latest updates

Cheers!

A-Math Integration of tan^2 x

Another question from O Level Additional Mathematics (A-Math).

lijun(: said...
i came across this qu that day, and i really want to clarify if the method i used is correct or not.int(tan^2x - x^3)

i changed it to int(sec^2x - 1 - x^3) instead, cos i don't think we can integrate tan.

is that feasible?

Absolutely. Since tan^2 x can't be integrated, you must think of alternative by making use of the relationship of tan^2 x + 1 = sec^2 x