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Print out the graphic organizer for derivatives and use the provided answer key to fill out your own.

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Complete the following circuit. Start with question #1. Solve it, and find the answer in another square. This will then be question #2. Keep going until you have looped back around to question #1. I'll post worked-out solutions next week!

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Watch the youtube video to check your answers to the "Basic Integration Worksheet" from last week.

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Keep a record of what you work on every day!  This will help you keep yourself on track!  Print this tracker and fill it out every day!

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Read through the following review lesson on Integrals. Take the "your turn" 10-question quiz at the bottom. Record your quiz results on your "Math log" for the day you took it.

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Integration

Integration can be used to find areas, volumes, central points and many useful things. It is often used to find the area underneath the graph of a function and the x-axis.

The first rule to know is that integrals and derivatives are opposites!

Sometimes we can work out an integral,
because we know a matching derivative.

Integration Rules

Here are the most useful rules, with examples below:

Examples

Example: what is the integral of sin(x) ?

From the table above it is listed as being −cos(x) + C

It is written as:

∫sin(x) dx = −cos(x) + C

Example: what is the integral of 1/x ?

From the table above it is listed as being ln|x| + C

It is written as:

The vertical bars || either side of x mean absolute value, because we don't want to give negative values to the natural logarithm function ln.

Power Rule

The question is asking "what is the integral of x 3 ?"

We can use the Power Rule, where n=3:

Example: What is ∫√x dx ?

√x is also x0.5

We can use the Power Rule, where n=0.5:

Multiplication by constant

We can move the 6 outside the integral:

And now use the Power Rule on :

Simplify:

Sum Rule

Example: What is ∫(cos x + x) dx ?

Use the Sum Rule:

Work out the integral of each (using table above):

Difference Rule

Example: What is ∫(ew − 3) dw ?

Use the Difference Rule:

Then work out the integral of each (using table above):

Sum, Difference, Constant Multiplication And Power Rules

Use the Sum and Difference Rule:

Constant Multiplication:

Power Rule:

Simplify:

Integration by Parts

See Integration by Parts

Substitution Rule

See Integration by Substitution

Final Advice

Get plenty of practice

Don't forget the dx (or dz, etc)

Don't forget the + C

6834, 6835, 6836, 6837, 6838, 6839, 6840, 6841, 6842, 6843

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Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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Practice these basic integrals.  Remember, rewrite first if there is a radical or you have to multiply.  Then, add 1 to the exponent and then divide by that exponent. Record your time spent on your math log.

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You can print this worksheet out and practice the problems.  The answer key is also included.  I'll post a video in a couple days with explanations.