Definite integrals and area under a curveAQA A-Level Maths: Mind map

Exam questions on Definite integrals and area under a curve

1. The curve $C_1$ has equation $y=3x^2-2x+4$.
   Explain why $\int_1^3\left(3x^2-2x+4\right)dx$ is equal to the area of the region bounded by $C_1$, the $x$-axis and the lines $x=1$ and $x=3$.2 marks
2. The curve $C_2$ has equation $y=(x-1)(x-5)$. The finite region $R$ is bounded by $C_2$ and the $x$-axis.
   Find the area of the finite region bounded by $C_2$, the coordinate axes and the line $x=1$.2 marks
3. The curve $C_3$ has equation $y=4x-x^3$.
   Find the coordinates of the points where $C_3$ meets the $x$-axis.3 marks