Evaluate the Integral integral of 3sin(x) with respect to x

Problem

(∫_^)(3*sin(x)*d(x))

Solution

1. Identify the constant multiple in the integrand.

2. Apply the constant multiple rule for integration by moving the 3 outside the integral.

(∫_^)(3*sin(x)*d(x))=3*(∫_^)(sin(x)*d(x))

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

3*(∫_^)(sin(x)*d(x))=3*(−cos(x))+C

4. Simplify the expression by multiplying the constant by the trigonometric term.

3*(−cos(x))+C=−3*cos(x)+C

Final Answer

(∫_^)(3*sin(x)*d(x))=−3*cos(x)+C

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