Find the Antiderivative 4sin(x)

Problem

(∫_^)(4*sin(x)*d(x))

Solution

1. Identify the integral as a constant multiple of a trigonometric function.

2. Apply the constant multiple rule for integration by moving the constant 4 outside the integral.

(∫_^)(4*sin(x)*d(x))=4*(∫_^)(sin(x)*d(x))

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

4*(∫_^)(sin(x)*d(x))=4*(−cos(x))+C

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

4*(−cos(x))+C=−4*cos(x)+C

Final Answer

(∫_^)(4*sin(x)*d(x))=−4*cos(x)+C

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