Integrating standard functionsEdexcel International A Level Maths: Mind map

Exam questions on Integrating standard functions

1. The function $f$ is defined by $f(x)=6e^{2x}-\frac{3}{x}$ for $x>0$.
   The curve $y=F(x)$ has gradient $f(x)$ and passes through the point $(1,3e^2+5)$. Find $F(x)$.2 marks
2. The function $g$ is defined by $g(x)=4\sin 3x+2\cos\frac{x}{2}$, where $x$ is in radians.
   Given that $\frac{dF}{dx}=g(x)$ and $F(0)=0$, find the exact value of $F(\pi)$.2 marks
3. A particle moves along a straight line. Its velocity is $v=3e^{-0.5t}+2$ m s$^{-1}$ at time $t$ seconds, for $t\geq0$, and its position relative to a fixed point $O$ is $s$ metres.
   Find the displacement of the particle between $t=0$ and $t=4$, giving your answer to 3 significant figures.3 marks