Federal income tax

Definition

Federal income tax is a tax levied by the United States Internal Revenue Service (IRS) on the annual earnings of individuals, corporations, trusts, and other legal entities. It is calculated based on the amount of taxable income earned during a calendar year.

5 Must Know Facts For Your Next Test

1. Federal income tax can be expressed as an integral where the rate of change of taxable income over time is analyzed.
2. The net change theorem can be applied to determine the total federal income tax paid over a period by integrating the marginal tax rates.
3. Marginal tax rates are piecewise functions, meaning they vary depending on different brackets of taxable income.
4. Integration techniques such as substitution may be needed to solve for total taxes when dealing with complex marginal rate functions.
5. Understanding definite integrals is crucial for calculating exact amounts owed or refunded in federal income taxes.

Review Questions

• How can the net change theorem be used to calculate total federal income tax?
• Explain how marginal tax rates create a piecewise function for integration purposes.
• What integration technique might you use if given a complex function representing federal income tax rates?

Related terms

Marginal Tax Rate: The rate at which the last dollar of taxable income is taxed, often represented as a piecewise function in calculus.

Net Change Theorem: \text{The theorem states that } \int_a^b f'(x) \ dx = f(b) - f(a), \text{ used to calculate total changes over an interval.}

Definite Integral: \text{An integral } \int_a^b f(x) \ dx \text{ representing the area under a curve from } x=a \text{ to } x=b.