This reference table pairs graphs with standard integral formulas:
>Area bounded by x-axis: Area = ∫_b^a f(x) dx
>Area bounded by y-axis: Area = ∫_c^d f(y) dy
>Area between two curves: Area = ∫_b^a [f(x) − g(x)] dx
>Volume of revolution about x-axis (disk method): Volume = π ∫_b^a y² dx
>Volume of revolution about y-axis (disk method): Volume = π ∫_c^d x² dx
Real-life applications: These formulas are used to calculate total accumulated quantities such as distance traveled from velocity curves, enclosed regions in economics and biology, and volumes of three-dimensional objects like tanks, pipes, vases, and machine parts in engineering and manufacturing.