| > | restart; |
| > | with( Student[Calculus1] ); |
| > |
| > | f := x/(x^4+1); |
| > |
| > | A := 0; |
| > | B := 4; |
| > | N := 4; |
| > |
| > | ApproximateInt(f, A..B, partition = N, method = left, output = sum); |
| > | ApproximateInt(f, A..B, partition = N, method = left, output = plot); |
![[Plot]](images/FTCdemo_11.gif)
| > |
| > | ApproximateInt(f, A..B, partition = N, method = midpoint, output = sum); |
| > | ApproximateInt(f, A..B, partition = N, method = midpoint, output = plot); |
![[Plot]](images/FTCdemo_13.gif)
| > |
| > | ApproximateInt(f, A..B, partition = N, method = right, output = sum); |
| > | ApproximateInt(f, A..B, partition = N, method = right, output = plot); |
![[Plot]](images/FTCdemo_15.gif)
| > |
| > | ApproximateInt(f, A..B, partition = N, output = animation); |
![[Plot]](images/FTCdemo_16.gif)
| > |
| > | ApproximateInt(f, A..B, partition = n, method = left, output = sum); |
| > | limit( %, n=infinity ); |
| > | evalf( % ); |
| > |
| > | q1 := ApproximateInt(f, a..b, partition = n, method = left, output = sum); |
| > |
| > | #value( % ); |
| > | #simplify( %, n ); |
| > | #collect( %, n ); |
| > | q2 := limit( q1, n=infinity ); |
| > |
| > | F := int( f, x ); |
| > | q3 := eval( F, x=b ) - eval( F, x=a ); |
| > | q4 := int( f, x=a..b ); |
| > |
| > |