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Integration The Converse of Differentiation. If the curve passes through (1, -2), find the equation of the curve. The curve passes through (1,-2) Is a.

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Presentation on theme: "Integration The Converse of Differentiation. If the curve passes through (1, -2), find the equation of the curve. The curve passes through (1,-2) Is a."— Presentation transcript:

1 Integration The Converse of Differentiation

2 If the curve passes through (1, -2), find the equation of the curve. The curve passes through (1,-2) Is a differential equation Is the general solution Is a particular solution Note: Return to main

3 If the minimum value of y is 2½, find the equation of the curve. Hence the curve passes through (-3, 2½ ) Return to main

4 Calculate the area of the pond covered by the ripples after 9 seconds. We solve this differential equation from the conditions given. What are the initial conditions? When t=0, the stone has just dropped, A=0 Hence: c=0 At time t=9: A=162m 2

5 Return to main

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