Evaluate the Integral

Problem

(∫_0^1)(1/(1+x2)*d(x))

Solution

1. Identify the antiderivative of the integrand 1/(1+x2) which is the inverse tangent function, arctan(x)

2. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper and lower limits of integration.

(∫_0^1)(1/(1+x2)*d(x))=[arctan(x)]10

3. Substitute the upper limit 1 and the lower limit 0 into the expression.

arctan(1)−arctan(0)

4. Evaluate the trigonometric values where arctan(1)=π/4 and arctan(0)=0

π/4−0

5. Simplify the result to find the final value.

π/4

Final Answer

(∫_0^1)(1/(1+x2)*d(x))=π/4

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