Evaluate the Integral integral of pisin(pix) with respect to x

Problem

(∫_^)(π*sin(π*x)*d(x))

Solution

1. Identify the constant factor π and move it outside the integral.

π*(∫_^)(sin(π*x)*d(x))

2. Apply the rule for the integral of sin(a*x) which is −1/a*cos(a*x)

π*(−1/π*cos(π*x))+C

3. Simplify the expression by canceling the π in the numerator and denominator.

−cos(π*x)+C

Final Answer

(∫_^)(π*sin(π*x)*d(x))=−cos(π*x)+C

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