Difference between revisions of "Definite Integral"
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[[Category:Calculus]] | [[Category:Calculus]] | ||
+ | |||
+ | === Objectives === | ||
+ | To enable students to, | ||
+ | # understand the process of anti-differentiation.; | ||
+ | # recognize the problem of calculating areas bounded by non-linear function; | ||
+ | # understand how the limit of the sum of rectangles may be used to calculate the area bounded by a function; | ||
+ | # understand the meaning of <math>\textstyle \int\limits_{a}^{b} \displaystyle f(x)dx</math>; | ||
+ | # calculate the area under a function between two extremes; | ||
+ | # apply knowledge and skills relating to anti-differentiation to solve problems; | ||
+ | # verify that the area bounded by the curve y=f(x), x=a, x=b and x-axis =<math>\textstyle \int\limits_{a}^{b} \displaystyle f(x)dx</math> | ||
+ | |||
+ | === Prerequisites/Instructions, prior preparations, if any === | ||
+ | Knowledge on plotting graphs, differentiation, mapping and computing functions. | ||
=== Geogebra Resources === | === Geogebra Resources === | ||
Line 5: | Line 18: | ||
# [[:File:Geometrical interpretation of definite integral.ggb#catlinks|File:Geometrical interpretation of definite integral.ggb]] | # [[:File:Geometrical interpretation of definite integral.ggb#catlinks|File:Geometrical interpretation of definite integral.ggb]] | ||
# [[:File:Property of definite integrals.ggb]]{{Geogebra|bxkhhvjy}} | # [[:File:Property of definite integrals.ggb]]{{Geogebra|bxkhhvjy}} | ||
+ | |||
+ | === Process === | ||
+ | |||
+ | === Evaluation === | ||
+ | Evaluate following Definite integrals and give their geometrical interpretation: | ||
+ | # <big>''<math display="inline">\int\limits_{2}^{5} (x + 1) dx</math>''</big> | ||
+ | # <big><math display="inline">\int\limits_{2}^{3} x dx</math></big> | ||
+ | # <big><math display="inline">\int\limits_{1}^{4} (x^2 - x) dx</math></big> |
Revision as of 17:40, 5 June 2021
Objectives
To enable students to,
- understand the process of anti-differentiation.;
- recognize the problem of calculating areas bounded by non-linear function;
- understand how the limit of the sum of rectangles may be used to calculate the area bounded by a function;
- understand the meaning of ;
- calculate the area under a function between two extremes;
- apply knowledge and skills relating to anti-differentiation to solve problems;
- verify that the area bounded by the curve y=f(x), x=a, x=b and x-axis =
Prerequisites/Instructions, prior preparations, if any
Knowledge on plotting graphs, differentiation, mapping and computing functions.
Geogebra Resources
Download this geogebra file from this link.
Download this geogebra file from this link.
Process
Evaluation
Evaluate following Definite integrals and give their geometrical interpretation: