Difference between revisions of "Definite Integral"

Revision as of 17:40, 5 June 2021

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 $\textstyle \int \limits _{a}^{b}\displaystyle f(x)dx$ ;
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 = $\textstyle \int \limits _{a}^{b}\displaystyle f(x)dx$

Knowledge on plotting graphs, differentiation, mapping and computing functions.

Download this geogebra file from this link.

Evaluate following Definite integrals and give their geometrical interpretation:

@@ Line 1: / Line 1: @@
 [[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 ===
@@ Line 5: / Line 18: @@
 # [[:File:Geometrical interpretation of definite integral.ggb#catlinks|File:Geometrical interpretation of definite integral.ggb]]
 # [[: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>