Bài tập Toán INTEGRATION 09

Created by T Madas Question 19 The gradient of every point on the curve C , with equation y = f ( x ) , satisfies f ′ ( x ) = 3x − x + k , where k is a constant The points P ( 0, −3) and Q ( 2,7 ) both lie on C Find an equation for C y = x3 − x + x − Created by T Madas Created by T Madas Question 20 y R C Q P O x The figure above shows the curve C which meets the coordinates axes at the points P , Q and R Given the gradient function of C is given by f ′( x) = − 4x , and that f (1) = f ( ) , determine the coordinates of P , Q and R ( ) P ( −1, ) , P , , R ( 0,5 ) Created by T Madas Created by T Madas Question 21 The curve C with equation y = f ( x ) satisfies f ′( x) = − x2 , x ≠ a) Given that f (1) = , find an expression for f ( x ) b) Sketch the graph of f ( x ) , indicating clearly the asymptotes of the curve and the coordinates of any points where the curve crosses the coordinate axes f ( x) = −2 , x ( 2,0 ) Question 22 −1  f ( x ) =  x −   x −  , x >    Show clearly that ∫ f ( x ) dx = P x + Qx + Rx + C , where P , Q and R are integers to be found, and C is an arbitrary constant P = −8 , Q = 13 , R = −2 Created by T Madas