Integration as the reverse of differentiationEdexcel A-Level Maths: Mind map

Exam questions on Integration as the reverse of differentiation

1. A curve has gradient function $\frac{dy}{dx}=6x^{2}-4x+5$ and passes through the point $(1,7)$.
   Find the $y$-coordinate of the point on the curve where $x=2$.2 marks
2. A curve $y=f(x)$, for $x>0$, has gradient function $f'(x)=\frac{(x-1)^{2}}{\sqrt x}$ and passes through the point $(1,2)$.
   Find an equation of the curve.2 marks
3. A curve $y=f(x)$, for $x>0$, has gradient function $f'(x)=3x^{2}-\frac{6}{x^{3}}$ and passes through the point $(1,2)$.
   Find $f(x)$.3 marks