Evaluate the Integral

Problem

(∫_0^2*π)(cos(x)*d(x))

Solution

1. Identify the antiderivative of the function cos(x)

(∫_^)(cos(x)*d(x))=sin(x)

2. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper limit 2*π and the lower limit 0

(∫_0^2*π)(cos(x)*d(x))=[sin(x)](2*π)0

3. Substitute the limits into the expression.

sin(2*π)−sin(0)

4. Simplify the expression using trigonometric values, where sin(2*π)=0 and sin(0)=0

0−0=0

Final Answer

(∫_0^2*π)(cos(x)*d(x))=0

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