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Math  /  Calculus

Questionintegrate −sin⁡xdx-\sin x d x

Studdy Solution

STEP 1

1. The problem involves finding the indefinite integral of the function −sin⁡x-\sin x.
2. We will use basic integration rules for trigonometric functions.

STEP 2

1. Identify the integral form.
2. Apply the integration rule for −sin⁡x-\sin x.
3. Add the constant of integration.

STEP 3

Recognize the integral form. We need to integrate the function −sin⁡x-\sin x:
∫−sin⁡x dx\int -\sin x \, dx

STEP 4

Apply the integration rule for −sin⁡x-\sin x. The integral of sin⁡x\sin x is −cos⁡x-\cos x, so the integral of −sin⁡x-\sin x is:
∫−sin⁡x dx=cos⁡x\int -\sin x \, dx = \cos x

STEP 5

Add the constant of integration C C to the result, as this is an indefinite integral:
∫−sin⁡x dx=cos⁡x+C\int -\sin x \, dx = \cos x + C
The indefinite integral of −sin⁡x-\sin x is:
cos⁡x+C\boxed{\cos x + C}

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