Evaluate the Integral

Problem

(∫_^)(1/5*sin(5*x)*d(x))

Solution

1. Identify the constant factor and move it outside the integral to simplify the expression.

1/5*(∫_^)(sin(5*x)*d(x))

2. Apply the integration rule for the sine function, which states that (∫_^)(sin(a*x)*d(x))=−1/a*cos(a*x)+C

1/5*(−1/5*cos(5*x))+C

3. Multiply the fractions to find the final coefficient of the cosine term.

−1/25*cos(5*x)+C

Final Answer

(∫_^)(1/5*sin(5*x)*d(x))=−1/25*cos(5*x)+C

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