Evaluate the Integral integral of -cos(x) with respect to x

Problem

(∫_^)(−cos(x)*d(x))

Solution

1. Identify the constant factor in the integrand. The negative sign is equivalent to a constant of −1

2. Apply the constant multiple rule for integration, which allows the −1 to be moved outside the integral.

(∫_^)(−cos(x)*d(x))=−(∫_^)(cos(x)*d(x))

3. Recall the basic integration rule for the cosine function, which states that (∫_^)(cos(x)*d(x))=sin(x)+C

4. Substitute the result of the basic integral back into the expression and include the constant of integration C

−(sin(x))+C=−sin(x)+C

Final Answer

(∫_^)(−cos(x)*d(x))=−sin(x)+C

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