Changes
From Karnataka Open Educational Resources
1,137 bytes added
, 17:40, 5 June 2021
Line 1: |
Line 1: |
| [[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> |