Consider the Semicircle of Radius 4 Pictured Below $\int_{-4}^{4} \sqrt{16-x^{2}} d x$

question 161

Multiple Choice

Consider the semicircle of radius 4 pictured below.Which of the following could represent the area of the semicircle? Select all that apply.

• A) \(\int_{-4}^{4} \sqrt{16-x^{2}} d x\)
• B) \(\frac{1}{2} \cdot \pi \cdot 4^{2}\)
• C) \(4 \int_{-1}^{1} \sqrt{16+x^{2}} d x\)
• D) \(\left.\frac{1}{2}\left[x \sqrt{16-x^{2}}+16 \arcsin \left(\frac{x}{4}\right)\right]\right|_{-4} ^{4}\)
• E) \(\left.\frac{2}{4}\left[x \sqrt{16-x^{2}}\right]\right|_{-4} ^{4}\)

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Definitions:

Proportional Tax

A tax system where the tax rate remains constant regardless of the amount subject to tax, causing taxpayers to pay the same percentage of their income irrespective of its size.

Deductions

Expenses subtracted from gross income to determine the taxable income.

Excise Tax

A tax levied on certain goods, services, and activities, such as tobacco, alcohol, and fuel, usually to discourage their consumption and raise government revenue.

Local Property Tax

A tax assessed on real estate properties, usually levied by local government entities such as cities or counties.