5.5 Integration and area under a curveIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What is \int ax^n\,dx (for n\neq-1)?
What is integration?
Why do we add +c?
Integrate 6x^2.
Integrate x^{-2}.
How do you check an integral?
How do you find c?
\frac{dy}{dx}=3x^2+x, y=10 when x=1. Find y.
What is \inta^b f(x)\,dx in terms of F?
Area between y=f(x)0, the x-axis, x=a, x=b?
What should you write first in an area question?
What does reversing the limits do?

Exam questions on 5.5 Integration and area under a curve

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
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
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

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).