Definite integrals and area under a curveEdexcel A-Level Maths: Flashcards

What these 12 flashcards ask

\inta^bf(x)\,dx in terms of F?
Is a constant c needed in a definite integral?
\intb^af(x)\,dx in terms of \inta^bf(x)\,dx?
Area under y=f(x) from x=a to x=b (curve above the axis)?
What does a negative definite integral tell you?
How do you find the total area when a curve crosses the x-axis?
Area between a curve and a line?
How do you find the limits for the area between a curve and a line?
\int0^4\left(6x-x^2\right)dx?
Area between y=6x-x^2 and y=2x?
\int1^3\left(x^2-4x+3\right)dx and the area it represents?
First step in any area question?

Exam questions on Definite integrals and area under a curve

The curve $C$ has equation $y=x^2-4x+3$ .
Find the total area bounded by $C$ , the $x$ -axis and the lines $x=0$ and $x=4$ .2 marks
The curve $C$ has equation $y=6x-x^2$ and the line $l$ has equation $y=2x$ . They meet at the origin $O$ and at the point $P$ .
Find the area of the finite region bounded by $C$ and $l$ .2 marks
The curve $C$ has equation $y=x^3-6x^2+8x$ .
Show that $C$ crosses the $x$ -axis at $x=0$ , $x=2$ and $x=4$ , and find $\int y\,\mathrm{d}x$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).