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Evaluate 718arctan(x)dx\int_{-7}^{18} \arctan (x) d x "Symbolically" (Plug in the Limits but Don't Evaluate)

Question 33

Multiple Choice

Evaluate 718arctan(x) dx\int_{-7}^{18} \arctan (x) d x "symbolically" (plug in the limits but don't evaluate) .Hint: Integrate by parts using ddxarctanx=11+x2\frac{d}{d x} \arctan x=\frac{1}{1+x^{2}} .


A) 18arctan187arctan(7) +ln(1+182) +ln(1+72) 18 \arctan 18-7 \arctan (-7) +\ln \left(1+18^{2}\right) +\ln \left(1+7^{2}\right)
B) 18arctan18+7arctan(7) ln(1+182) ln(1+72) 18 \arctan 18+7 \arctan (-7) -\ln \left(1+18^{2}\right) -\ln \left(1+7^{2}\right)
C) 18arctan187arctan(7) +12ln(1+182) 12ln(1+72) 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) 18arctan18+7arctan(7) 12ln(1+182) +12ln(1+72) 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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