Labware - MA35 Multivariable Calculus - Single Variable Calculus

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Area under a Function Graph

Text

Integrals are interpreted geometrically as the area under a function graph.

Specifically, for some variable x, a function f(x), and constants a and b, the integral

abf(x)dx

is interpreted as the area between the x-axis and portions of the graph of f(x) for which y > 0 minus the area between the x-axis and portions of the graph of f(x) for which y < 0.

Demos

Exercises

  • Use the demo to estimate the values of the following integrals:
    • 011dx
    • 01xdx
    • -11x2dx
    • 01-1dx
    • -11x3dx