Integration

Area between Two Curves _ Integration

Applet

Steps for constructing the applet

1.Open a new geogebra file
2.Create 3 sliders on number and give names a, c and m ( min: 0, Max : 10, Incr: 0.1 )
3.Create the function f ( f(x) = ax2 by typing in the Input field f(x) = a*x^2
4.Create the function g ( g(x) = mx + c by typing in the Input field g(x) = m*x + c
5.Mark the intersecting points A and B between the curve and the line using the tool Intersect Two objects
Continue

Derivative and Tangent of Sin(x)
Click here for the applet
1. Insert the function f(x) = sin(x) into the input field and press enter key.
2. Create a point A on f.
3. Use the tool Tangents and click on the point A and on the function f. Change the tangents name to t
4. Type the command s = Slope[t] into the input field and press enter key. Use the move tool to drag the point A with the mouse and observe the movement of the tangent.
5. Type B = (x(A), s) into the input field and press enter key.
6. Right click on the new point B and give tick mark (switch on ) on Trace on button.
7. Use the move tool and drag A with the mouse. Then B will leavea trace.
8. Type the command Derivative[f] into the input field.
9. Use the move tool and drag A with the mouse and observe the movement.
10. Save the construction.

Basic Constructions in Geogebra

Construction of Circumcircle of a Triangle

Draw a triangle and construct its circumcircle.

1.Using the Polygon tool construct triangle ABC.
2.Using Perpendicular bisector tool draw perpendicular bsectors to any two sides of the triangle.
3.Mark the intersecting point of the perpendicular bisectors which is the centre of the circumcrcle. ( Intersect Two Objects tool)
4.Choose the tool Circle with centre through point and click first at the centre, then at any vertex of the triangle.
5.Using the Move tool change the position of vertices.
6.Save the construction.

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