Find the equation of the curve with the given derivative of y with respect to x that
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Find the equation of the curve with the given derivative of y with respect to x that passes through the given point:
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D с e dy dx dy d.x dy dx = 3x² + 2x; = √x + = x²; = (x + 2)²; point (2, 10) point (4, 11) point (1,7) b d f dy dx = 4x³ + dy 3 dx √x = +33- dy dx √x = X; x² + 3 + 3; point (1,4) point (4,0) point (0, 1)
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a dydx 3x 2x Integrating both sides wrt x dydx dx dy 3x 2x c c is the constant of integration or y 3x 3 2x 2 c x x c Since the curve passes through P2 10 P satisfies the equation 10 2 2 c or c 10 8 4 2 y x x 2 b dydx 4x 2x 3 Integrating both sides wrt x dydx dx dy 4x dx 2x dx 3 dx c c is the constant of integration or y 4x 4 4 2x 3 dx 3x c x 4 2x 2 2 3x c x 4 x 2 3x c To evaluate c substitute the coordinates of point P1 4 in the obtained equation or 4 1 1 3 c or c 1 y x 4 1 x 3x 1 c dydx x 14 x Integrating both sides wrt x y x dx 14 x dx c c is the constant of integration or y x dx 14 x dx c x 121 121 14 x dx c 23 x 32 14 x 3 c 23 x 32 112 x c As the curve passes through P4 11 therefore P satisfies the equation or 11 23 4 32 112 4 c or c 11 163 163 13 y 23 x 32 112 x 13 d dydx 3x x Integrating both sides wrt x y 3 1 x dx x dx c c is the constant of integration or y 3 ...View the full answer
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Related Book For
Edexcel AS And A Level Mathematics Pure Mathematics Year 1/AS
ISBN: 9781292183398
1st Edition
Authors: Greg Attwood
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