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Sample problem, #10, Lesson 4.9
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Find the most general antiderivative of the function. Check your answer using differentiation.
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Given problem, #10, Lesson 4.9 |
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Using our knowledge of derivatives, we find the antiderivative. |
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We check our work by taking the derivative of our antiderivative. We see that we have arrived back at the function we began with. |
Sample problem, #16, Lesson 4.9
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Find f
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Given problem, #16, Lesson 4.9 |
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We use our derivative knowledge to calculate the antiderivative two times. The last line has some algebraic simplification. |
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We check our work by starting at our answer and differentiating twice. We see that our work must have been done correctly, because we have arrived back at our starting problem. |
Sample problem, #36, lesson 4.9
A particle moves with acceleration
function  . Its initial velocity is  m/s and its initial displacement is  m. Find its position after t
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Given problem, #36, lesson 4.9 |
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First we integrate the acceleration function. This results in a general form of the velocity equation. |
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Because we were given the initial velocity, we can solve for C and get the complete velocity equation. |
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Now we integrate the velocity formula to get the general position formula. Given the intial position of 10, we can arrive at the position formula at any value for t. |
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1-41, Odds
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