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

Problem

(∫_^)(−sin(x)*d(x))

Solution

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

2. Apply the constant multiple rule for integration to move the negative sign outside the integral.

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

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

4. Substitute the result of the integral back into the expression.

−(−cos(x))+C

5. Simplify the signs. The two negatives cancel out to become positive.

cos(x)+C

Final Answer

(∫_^)(−sin(x)*d(x))=cos(x)+C

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