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From Karnataka Open Educational Resources
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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 ===
# [[: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>
