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:

Bond

A financial instrument where an investor loans money to an entity (corporate or governmental) that borrows the funds for a defined period at a variable or fixed interest rate.

Stockholders' Equity

Stockholders' equity represents the ownership interest of shareholders in the net assets of a company, calculated as the company's total assets minus its total liabilities.

Bonds Payable

A long-term financial liability where the issuer is obligated to pay back the principal along with interest to the bondholders at a future date.

Book Value

The net value of a company's assets minus its liabilities, often used to assess the company’s financial health.