Get in touch with the [i]integral[/i] command.
[table][tr][td]1.[/td][td]Define the function [math]f\left(x\right)=x^2[/math] by entering the equation of the function into the [i]Input Bar[/i]. [/td][/tr][tr][td]2.[/td][td]Calculate the indefinite integral of [i]f(x)[/i] using the command [math]Integral\left(f\right)[/math].[/td][/tr][tr][td][/td][td][b]Hint:[/b] You can use the [math]\int[/math]-key on the virtual keyboard to enter the [i]Integral [/i]command. [/td][/tr][tr][td][br][/td][td][b]Note: [/b]The [i]GeoGebra CAS Calculator [/i]gives you as output a primitive of [i]f(x)[/i] with an additive constant [i]c[sub]1[/sub][/i].[/td][/tr][tr][td]3.[/td][td]Calculate the definite integral of [i]f(x) [/i]between 0 and 3 with the command [math]Integral\left(f,0,3\right)[/math].[/td][/tr][tr][td]4.[/td][td]Calculate the definite integral of [i]f(x) [/i]between 0 and b with the command [math]Integral\left(f,0,b\right)[/math].[/td][/tr][tr][td]5.[/td][td]Calculate the definite integral of [i]f(x) [/i]between a and b with the command [math]Integral\left(f,a,b\right)[/math].[/td][/tr][/table]
Determine other definite, indefinite and improper integrals.
[table][tr][td]1.[/td][td]Define the function [math]g(x)=cos(x)\cdot sin\left(x\right)[/math] by entering the equation of the function into the [i]Input Bar[/i]. [/td][/tr][tr][td]2.[/td][td]Determine a primitive of [i]g(x) [/i]using the command [math]Integral(g)[/math].[/td][/tr][tr][td][br][/td][td][b]Hint:[/b] [b][/b]You can use the [math]\int[/math]-key on the virtual keyboard to enter the [i]Integral [/i]command. [/td][/tr][tr][td]3.[/td][td]Calculate the definite integral of [i]g(x)[/i] between 0 and [math]\frac{\pi}{2}[/math] using the command [math]Integral\left(g,0,\frac{\pi}{2}\right)[/math].[/td][/tr][tr][td]4.[/td][td]Define the function [math]h(x)=x^2\cdot e^{^{-x}}[/math] by entering the equation of the function into the [i]Input Bar[/i]. [/td][/tr][tr][td]5.[/td][td]Determine the indefinite integral of [i]h(x)[/i] by entering [math]Integral\left(h\right)[/math].[/td][/tr][tr][td]6.[/td][td]Calculate the improper integral of [i]h(x)[/i] between 0 and [math]\infty[/math] using the command [math]Integral\left(h,0,\infty\right)[/math].[br][b]Hint:[/b] To enter [math]\infty[/math], use the word [i]infinity[/i].[/td][/tr][/table][table][tr][td][/td][/tr][/table]