Vault Of Euclid

Area Under a Rational Function Using Partial Fractions

Logarithmic and exponential functions core

Find the area under \( y=1/(1-x^2) \) between \( x=0 \) and \( x=\frac{1}{2} \).

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What you need first

Integration of 1/x
Partial fraction decomposition
Properties of logarithms
The Fundamental Theorem of Calculus

What this problem tests

Tests the ability to perform partial fraction decomposition on a simple rational function and correctly evaluate the resulting logarithmic terms.

This is a standard Calculus II problem introducing the application of partial fractions to definite integrals.

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