Find the Integral -cos(x)

Problem

(∫_^)(−cos(x)*d(x))

Solution

1. Identify the constant multiple rule for integration, which allows the negative sign to be moved outside the integral.

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

2. Apply the basic integration rule for the cosine function, which states that the integral of cos(x) is sin(x)

(∫_^)(cos(x)*d(x))=sin(x)+C

3. Combine the results by multiplying the integral by the negative sign and adding the constant of integration C

−(sin(x))+C=−sin(x)+C

Final Answer

(∫_^)(−cos(x)*d(x))=−sin(x)+C

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