Finding indefinite integrals of functions.
Integrate eˣ, 1/x and trig functions
Recognise the reverse chain rule patterns
Working with definite integrals and their applications.
Calculating areas under curves using integration.
Write an equal-width rectangle sum and its limiting integral
Using substitution to evaluate integrals.
State and apply the integration by parts formula
Split a rational function into partial fractions
Integrate sin²x and cos²x
Derive and use $\int y\,dx=\int y(t)x'(t)\,dt$
Recognise a first-order differential equation of the form $\dfrac{dy}{dx}=f(x)g(y)$
Translate a worded rate into a differential equation
Work through each topic to complete the section.