Bài tập CALCULUS 02

Created by T Madas Question (**) y y = ( − x )( x + 1) O x The figure above shows the curve with equation y = ( − x )( x + 1) , x ∈ » Find the exact area of the region, bounded by the curve and the x axis, shown shaded in the figure above MP1-M , area = 32 Created by T Madas Created by T Madas Question (**) y = 2x2 − x + x3 , x ≠ Find a fully simplified expression for  y dx C1A , x3 + x −2 + x + C Question (**) f ( x ) = x2 − x + 1, x ∈ » Find the coordinates of the point on the curve with equation y = f ( x ) , whose gradient is ( 3, −2 ) Created by T Madas Created by T Madas Question (**) y = x3 − x + 12 , x ∈ » Find the range of values of x for which y is decreasing C2E , < x < Question (**) y y = ( x + 1)( x − )( x − ) x O The figure above shows the curve with equation y = ( x + 1)( x − )( x − ) , x ∈ » a) Write the equation of the curve in the form y = x3 + ax + bx + c , where a , b and c are constants b) Find the exact area the shaded region C2D , y = x3 − x + x + , area = 16 Created by T Madas