This is a common type of question which involves using rectangles of equal width to estimate the area under the curve. There are two ways to draw the rectangles. One way will give you an underestimate of the exact area while the other way will give you an overestimate. In this question, both ways are explored and we zoom in on the approach of how to prove the total area of *n* number of rectangles is expressed in summation form.

# Integration Techniques

## Differential Equation Definitions & Problem

The main challenge in Differential Equation is formulating a differential equation from a problem situation and deriving its solution. It requires basic integration techniques as shown in the following question.

## Integration by Parts Formula Derivation & Examples

When students start learning Integration by Parts, they might not be able to remember the formula well. In fact, you do not need to rote memorise if you know that Integration by Parts can be derived in seconds from Differentiation Product Rule and I highly recommend you to do so via Product Rule until it comes to you naturally.

In this post, I show you the step by step to derive your Integration by Parts formula and examples to apply it.

## Integration Application: Volume

In this question, some students might face two challenges:

- How to find the volume of the shaded region
- How to apply the correct integration techniques (Click here for summary & examples) when we need to integrate trigonometric functions in product form and raised to certain powers like in this question

I will classify this question as a basic level and I hope you have learnt something new if you are not able to complete this question correctly.

## Integration Involving Modulus Function

In this question, we look at the application of integration techniques, particularly on how to integrate a modulus function. The strategy I use in this question is known as **Splitting. **For you to be able to split correctly, I would suggest sketching the modulus graph so that you know the correct equation to represent each portion of the modulus graph.

## Cover Up Rule for Partial Fractions

In MF15 and MF26, we are given the partial fractions decomposition for

- Non-repeated linear factors
- Repeated linear factors
- Non-repeated quadratic factor

It is useful to work with partial fractions especially when we do integration.

I have given 3 examples on how and when we use cover up rule (CUR). It acts like a shortcut to comparing coefficients. However, please note when CUR works and when we have to stick to our old good method of comparing coefficients.