Evaluate the Integral

Problem

(∫_0^π)(cos(x)*d(x))

Solution

1. Identify the integrand and the limits of integration. The function to integrate is cos(x) and the interval is [0,π]

2. Find the antiderivative of the function cos(x) The antiderivative of cos(x) is sin(x)

3. Apply the Fundamental Theorem of Calculus, which states that (∫_a^b)(ƒ(x)*d(x))=F(b)−F(a) where F is the antiderivative.

4. Substitute the upper limit π into the antiderivative.

sin(π)=0

5. Substitute the lower limit 0 into the antiderivative.

sin(0)=0

6. Subtract the value at the lower limit from the value at the upper limit.

0−0=0

Final Answer

(∫_0^π)(cos(x)*d(x))=0

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