Evaluate the Integral

Problem

(∫_π/6^π)(sin(x)*d(x))

Solution

1. Identify the integral as a definite integral of the sine function.

2. Apply the Fundamental Theorem of Calculus by finding the antiderivative of sin(x) which is −cos(x)

3. Evaluate the antiderivative at the upper limit of integration, π

−cos(π)=−(−1)=1

4. Evaluate the antiderivative at the lower limit of integration, π/6

−cos(π/6)=−√(,3)/2

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

1−(−√(,3)/2)=1+√(,3)/2

6. Simplify the expression into a single fraction.

(2+√(,3))/2

Final Answer

(∫_π/6^π)(sin(x)*d(x))=(2+√(,3))/2

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