5.11 Further integrationIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

\int x^n\,dx for n\neq-1?
\int\dfrac1x\,dx?
\int\sin x\,dx and \int\cos x\,dx?
\int\dfrac{1}{\cos^2x}\,dx?
\int e^x\,dx?
\int f(ax+b)\,dx?
\int\sin(2x+5)\,dx?
\int\dfrac{1}{3x+2}\,dx?
Which substitution for \int4x\sin x^2\,dx?
\int\dfrac{\sin x}{\cos x}\,dx?
How do you change limits in a substitution?
What is \inta^bf(x)\,dx in terms of F?
How do you find the constant c?

Exam questions on 5.11 Further integration

Water flows into a tank at a rate of $r(t)=6\sqrt{t}$ litres per minute, where $t$ is the time in minutes since the flow started. The tank is empty when $t=0$ .
Find the time taken for the volume of water in the tank to reach $500$ litres.2 marks
The population of a colony of bacteria changes at a rate $\dfrac{dP}{dt}=\dfrac{12}{3t+2}$ thousand per hour, where $t$ is the time in hours and $t\ge0$ . At $t=0$ the population is $5$ thousand.
Find the time at which the population reaches $20$ thousand.2 marks
A particle moves in a straight line. At time $t$ seconds its velocity is $v=4t\sin(t^2)$ m s $^{-1}$ , where the angle is in radians. The displacement $s$ from the starting point is $0$ when $t=0$ .
Find an expression for $s$ in terms of $t$ .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).