Antiderivatives.What is the antiderivative of sin3x?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the anti derivative of sin 3x

Int [ sin 3x dx]

Let 3x = y => dx = dy / 3

=> Int [ (1/3)*sin y dy]

=> (1/3)*(-cos y)

=> (-1/3)* cos 3x + C

The anti derivative is (-1/3)* cos 3x + C

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To find the antiderivative of sin 3x, we'll have to determine the indefinite integral of sin 3x.

Int sin 3x dx

We'll substitute 3x by t.

3x = t

We'll differentiate both sides:

3dx = dt

We'll divide by 3:

dx = dt/3

We'll re-write the integral of the function , changing the variable x to t:

Int sin t*(dt/3) = (1/3)*Int sin t dt

(1/3)*Int sin t dt = - cos t/3 +C

We'll substitute t by 3x:

Int sin 3x dx =  - (cos 3x)/3 +C

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