Definite integrals and area under a curveEdexcel International A Level Maths: Mind map

Exam questions on Definite integrals and area under a curve

1. The curve $C$ has equation $y=3x^2-2x+1$, and $C$ lies above the $x$-axis for all values of $x$.
   Hence find the area of the region bounded by $C$, the $x$-axis and the lines $x=-1$ and $x=2$.2 marks
2. The curve $C$ has equation $y=x^2-4x+3$ and crosses the $x$-axis at $A(1,0)$ and $B(3,0)$.
   Find the total area of the regions bounded by $C$, the $x$-axis, the $y$-axis and the line $x=3$.2 marks
3. The curve $C$ has equation $y=3\sqrt{x}+\frac{2}{x^2}$, for $x>0$.
   Find $\int y\,dx$.3 marks