Evaluate the Integral

Problem

(∫_0^1)(1/√(,1−x2)*d(x))

Solution

1. Identify the integrand as the derivative of the inverse sine function, arcsin(x)

2. Apply the Fundamental Theorem of Calculus by finding the antiderivative.

(∫_^)(1/√(,1−x2)*d(x))=arcsin(x)

3. Evaluate the antiderivative at the upper limit of integration, x=1

arcsin(1)=π/2

4. Evaluate the antiderivative at the lower limit of integration, x=0

arcsin(0)=0

5. Subtract the lower limit value from the upper limit value.

π/2−0=π/2

Final Answer

(∫_0^1)(1/√(,1−x2)*d(x))=π/2

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