Evaluate the Integral

Problem

(∫_0^π/2)(cos(x)*d(x))

Solution

1. Identify the integral as a definite integral of the function ƒ(x)=cos(x) over the interval [0,π/2]

2. Find the antiderivative of cos(x) which is sin(x) since the derivative of sin(x) is cos(x)

3. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper limit of integration and subtracting the value at the lower limit.

[sin(x)](π/2)0

4. Substitute the limits into the expression.

sin(π/2)−sin(0)

5. Evaluate the trigonometric values where sin(π/2)=1 and sin(0)=0

1−0

Final Answer

(∫_0^π/2)(cos(x)*d(x))=1

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