Evaluates areas and accumulated change, including integrals you can't do by hand.
In short: A definite integral gives the area between a curve and the x-axis over an interval, counting regions below the axis as negative. The GDC computes it from the function and the lower and upper limits. Use it to evaluate integrals and areas on calculator papers, and write the integral you entered in your working.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | MATH → 9:fnInt(f(x), x, a, b). Or graph and use 2nd → CALC → 7:∫f(x)dx. | Run-Matrix → MATH (F4) → ∫dx, then enter the function and limits. | menu → Calculus → Numerical Integral, or use the ∫ template. |
Tip: Area below the x-axis is negative - take the absolute value if the question asks for area.
Tip: A definite integral can return a negative value where the curve is below the x-axis - for total area, integrate the parts separately.
Tip: Area below the x-axis is negative - take the absolute value if the question asks for area.
Tip: A definite integral can return a negative value where the curve is below the x-axis - for total area, integrate the parts separately.
Tip: Area below the x-axis is negative - take the absolute value if the question asks for area.
Tip: A definite integral can return a negative value where the curve is below the x-axis - for total area, integrate the parts separately.
Here's a real IB-style question that uses exactly this technique.
Find the value of ∫₀³ (x² + 1) dx.
Evaluates areas and accumulated change, including integrals you can't do by hand. Finding the area under a curve between two x-values. The integral is difficult or impossible to find algebraically (e.g. involves eˣ²).
1. MATH → 9:fnInt(f(x), x, a, b). Or graph and use 2nd → CALC → 7:∫f(x)dx. 2. Enter the lower and upper limits to get the value.
1. Run-Matrix → MATH (F4) → ∫dx, then enter the function and limits. 2. Enter the lower and upper limits to get the value.
1. menu → Calculus → Numerical Integral, or use the ∫ template. 2. Enter the lower and upper limits to get the value.
Area below the x-axis is negative - take the absolute value if the question asks for area. A definite integral can return a negative value where the curve is below the x-axis - for total area, integrate the parts separately.
In the worked example on this page (3 marks, Paper 2), the marks are: M1: fnInt of x² + 1 from 0 to 3; A1: 12.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.