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

Exam questions on Integration as the reverse of differentiation

1. The gradient of the curve $C$ is given by $\frac{dy}{dx}=6x^2-4x+5$.
   Find the value of $y$ on $C$ when $x=2$.2 marks
2. The function $f$ satisfies $f'(x)=3\sqrt{x}+\frac{8}{x^2}$ for $x>0$, and $f(4)=20$.
   Find the value of $f(1)$.2 marks
3. The curve $C$ has gradient function $\frac{dy}{dx}=\frac{(x^2+3)^2}{x^2}$ for $x>0$.
   Find $\int\frac{dy}{dx}\,dx$.3 marks