5.5 Integration and area under a curveIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 5.5 Integration and area under a curve

1. Let $f(x)=6x^2-4x+3$. The graph of $y=g(x)$ has gradient function $f(x)$ and passes through the point $(1,5)$.
   Find $g(x)$.2 marks
2. A curve has equation $y=x^2+2$.
   Use your GDC to find the area of the region bounded by the curve, the $x$-axis and the lines $x=-1$ and $x=2$.2 marks
3. The gradient of a curve at the point $(x,y)$ is given by $\frac{dy}{dx}=4x^3-6x+\frac{5}{x^2}$, for $x>0$. The curve passes through the point $(1,4)$.
   Find an expression for $y$ in terms of $x$ and a constant $c$.3 marks