Evaluate $\int_{-7}^{18} \arctan (x) d x$ "Symbolically" (Plug in the Limits but Don't Evaluate)

question 33

Multiple Choice

Evaluate $\int_{-7}^{18} \arctan (x) d x$ "symbolically" (plug in the limits but don't evaluate) .Hint: Integrate by parts using $\frac{d}{d x} \arctan x=\frac{1}{1+x^{2}}$ .

• A) \(18 \arctan 18-7 \arctan (-7)+\ln \left(1+18^{2}\right)+\ln \left(1+7^{2}\right)\)
• B) \(18 \arctan 18+7 \arctan (-7)-\ln \left(1+18^{2}\right)-\ln \left(1+7^{2}\right)\)
• C) \(18 \arctan 18-7 \arctan (-7)+\frac{1}{2} \ln \left(1+18^{2}\right)-\frac{1}{2} \ln \left(1+7^{2}\right)\)
• D) \(18 \arctan 18+7 \arctan (-7)-\frac{1}{2} \ln \left(1+18^{2}\right)+\frac{1}{2} \ln \left(1+7^{2}\right)\)

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Definitions:

Interest Rate

The cost of borrowing money expressed as a percentage of the total amount loaned, paid by the borrower for the use of funds.

Equilibrium Interest

The interest rate at which the quantity of loanable funds demanded equals the quantity supplied, balancing savings and borrowing.

Loanable Funds

The money available for borrowing in the financial markets, influenced by interest rates and economic conditions.

Useful Life

The period during which an asset is expected to be usable for its intended purpose.