8.1 – Definite integrals
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Answers:
Solution:
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Example
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What happens when you Differentiate ?
What happens when you find Integration ?
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Different Forms of in Exponent Notation
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Different Forms of in Exponent Notation
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Answers:
Solution:
NNJR
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LFQ
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Plenary
Date:
Syllabus:
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LFQ
Topic: Definite Integral
LFQ: How do we integrate definite integrals and evaluate by applying upper limit and lower limit?
WILFs:
1. Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
2. Able to find out the constant from simple definite integral problem. (A/A*)
3. Able to find out the constant from complex definite integral problem.(A*)
Key Words:
I /We Do
Mini Plenary
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NNJR
LFQ
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Test Your Understanding
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Integration Notation
Integrate…
…this expression
Differentiate the following…
If you have multiple terms, you should use brackets. We’ll explore why when we encounter ‘definite’ integration.
Integrating Roots & Reciprocals
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Integrating Roots & Reciprocals
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Tip 2: Differentiate your answer to see if it gives the expression in the question.
Quickfire Coefficients
Expression | New Index | New Coefficient | Final Expression |
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Test Your Understanding
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Test Your Understanding
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Expand out brackets where possible, before integrating.
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Example
Test Your Understanding
Expand out brackets where possible, before integrating.
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Example
Test Your Understanding
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Test Your Understanding
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Example
Test Your Understanding
Test Your Understanding
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WILF: Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
Mini Plenary
You Do
Plenary
NNJR
I/We Do
LFQ
WILF: Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
Mini Plenary
You Do
Plenary
NNJR
I/We Do
LFQ
You need to be able to use the correct notation for Integration
Example Question
Find:
Integrate each part separately
Deal with the fractions
WILF: Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
Mini Plenary
You Do
Plenary
NNJR
I/We Do
LFQ
You need to be able to use the correct notation for Integration
This the the integral sign, meaning integrate
This is the expression to be integrated (brackets are often used to separate it)
The dx is telling you to integrate ‘with respect to x’
Example Question
Find:
Integrate each part separately
Deal with the fractions
WILF: Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
Mini Plenary
You Do
Plenary
NNJR
I/We Do
LFQ
You need to be able to integrate functions within defined limits
Your workings must be clear here. There are 3 stages…
The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
Example Question
Evaluate the following:
Integrate the function and put it in square brackets. Put the ‘limits’ outside the bracket.
Split the integration into 2 separate brackets
Substitute ‘b’ into the first, and ‘a’ into the second
Calculate the final value.
WILF: Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
Mini Plenary
You Do
Plenary
NNJR
I/We Do
LFQ
You need to be able to integrate functions within defined limits
Your workings must be clear here. There are 3 stages…
The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
Example Question
Evaluate the following:
Integrate the function and put it in square brackets. Put the ‘limits’ outside the bracket.
Split the integration into 2 separate brackets
Substitute ‘b’ into the first, and ‘a’ into the second
Calculate the final value.
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WILF: Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
Mini Plenary
You Do
Plenary
NNJR
I/We Do
LFQ
You need to be able to integrate functions within defined limits
Your workings must be clear here. There are 3 stages…
The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
Example Question
Evaluate the following:
Integrate the function and put it in square brackets. Put the ‘limits’ outside the bracket.
Simplify if possible
Split and substitute
WILF: Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
Mini Plenary
You Do
Plenary
NNJR
I/We Do
LFQ
You need to be able to integrate functions within defined limits
Your workings must be clear here. There are 3 stages…
The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
Example Question
Evaluate the following:
Integrate the function and put it in square brackets. Put the ‘limits’ outside the bracket.
Simplify if possible
Split and substitute
WILF: Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
Mini Plenary
You Do
Plenary
NNJR
I/We Do
LFQ
You need to be able to integrate functions within defined limits
Your workings must be clear here. There are 3 stages…
Example Question
Evaluate the following:
Sometimes you will have to simplify an expression before integrating
Integrate into Square Brackets
Simplify
Split into 2 and substitute b and a
WILF: Able to find upper limit and lower limit and subtract them to find the value of integrals. (B)
Mini Plenary
You Do
Plenary
NNJR
I/We Do
LFQ
You need to be able to integrate functions within defined limits
Your workings must be clear here. There are 3 stages…
Example Question
Evaluate the following:
Sometimes you will have to simplify an expression before integrating
Integrate into Square Brackets
Simplify
Split into 2 and substitute b and a
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The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
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The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
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The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
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44
The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
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45
The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
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The statement. Basically the function written out, with values for a and b
After integration. The function is integrated and put into square brackets
The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
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