Evaluate the Integral

Problem

(∫_0^π/4)(sin(x)*d(x))

Solution

1. Identify the antiderivative of the integrand sin(x)

(∫_^)(sin(x)*d(x))=−cos(x)

2. Apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper limit π/4 and the lower limit 0

[−cos(x)](π/4)0

3. Substitute the limits into the expression.

−cos(π/4)−(−cos(0))

4. Evaluate the trigonometric values.

−√(,2)/2−(−1)

5. Simplify the final numerical expression.

1−√(,2)/2

Final Answer

(∫_0^π/4)(sin(x)*d(x))=1−√(,2)/2

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