Find the Value of the Integral $\int _ { 0 } ^ { 1 } \ln \left( 1 + x ^ { 2 } \right) d x$

question 106

Multiple Choice

Find the value of the integral $\int _ { 0 } ^ { 1 } \ln \left( 1 + x ^ { 2 } \right) d x$

• A) \(\ln 2\)
• B) \(\frac { \pi } { 8 }\)
• C) \(\frac { \pi } { 2 } - 2 + \ln 2\)
• D) \(2 - \ln 2\)
• E) \(\frac { \pi } { 4 } + \ln 2\)
• F) \(\pi - 4\)
• G) \(\pi - 2\)
• H) \(\pi - \ln 2\)

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Definitions:

Bad Faith

Sartre’s characterization of a person’s refusal to accept himself or herself, particularly regarding the extent of his or her own freedom and limitations. This sometimes means not accepting the facts that are true about you. More often, it means accepting the facts about you as conclusive about your identity, as in the statement “Oh, I couldn’t do that, I’m too shy.”

Sartre

Jean-Paul Sartre, a French existentialist philosopher, playwright, novelist, political activist, and literary critic known for his work on existentialism and phenomenology.

Core Selves

The essential or most integral aspects of an individual's identity.

Identity Theorists

Identity Theorists in philosophy argue that mental states and brain states are exactly the same, in direct opposition to dualism.