IntegrationExercises on indefinite and definite integration of basic algebraic and trigonometric functions. 
This is level 8 ? Your answer should be a number (rounded to three significant figures if not exact) or a fraction in its lowest terms.
InstructionsTry your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. 




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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School: "We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory." Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset: "A set of real life savers!! 
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Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.  
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Level 1  Indefinite integration of basic polynomials with integer coefficient solutions
Level 2  Indefinite integration of basic polynomials with integer and fraction coefficient solutions
Level 3  Definite integration of basic polynomials
Level 4  Integration of expressions containing fractional indices
Level 5  Integration of basic trigonometric, exponential and reciprocal functions
Level 6  Integration of the composites of basic functions with the linear function ax + b
Level 7  Integration with the help of partial fractions
Level 8  Integration by substitution
Level 9  Integration by parts
Exam Style Questions  A collection of problems in the style of GCSE or IB/Alevel exam paper questions (worked solutions are available for Transum subscribers).
Differentiation  A multilevel set of exercises providing practice differentiating expressions
Use the ^ key to type in a power or index then the right arrow or tab key to end the power.
For example: Type 3x^2 to get 3x^{2}.
Use the forward slash / to type a fraction then the right arrow or tab key to end the fraction.
For example: Type 1/2 to get ½.
Fractions should be given in their lowest terms.
Answers to definite integral questions should be given as exact fractions or to three significant figures if the decimal answer does not terminate.
The following identities may also prove useful:
$$\sin^2x = \frac{1}{2}  \frac{1}{2} \cos 2x \text{ and } \cos^2x = \frac{1}{2} + \frac{1}{2} \cos 2x$$Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can doubleclick the 'Check' button to make it float at the bottom of your screen.
Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.
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