Chapter 13 - Integration Flashcards
What do you get when you integrate xn?
1 xn + 1 + c
n + 1
Add a power to x and divide by the new power
What do you get when you integrate kxn?
k xn + 1 + c
n + 1
Add 1 to the power of x and divide by that new power.
How do you integrate polynomials?
Apply the rules of integration separately to each term (expand and simplify first if needed to get into a polynomial format)
What do you get when you integrate (f’(x) +/- g’(x))?
f(x) +/- g(x) + c
ie. integrate each function separately in turn.
How do you find the constant of integration (“c”) ?
- Integrate the function
- Sub the given values (x, y) of a point on the curve, or the value of the function at a given point f(x) = k, into the integrated function.
- Solve the equation to find c
How do you calculate the definite integral?
- Integrate the function
- Write the integrated function in square brackets [f(x)]ba
- Evaluate f(b) - f(a)
How do you calculate the area between a positive curve, the x-axis, and the lines x = a and x = b?
- Write the definite integral statement with limits x = a and x = b
- Integrate the function and write the integral in square brackets with limits a and b
- Evaluate the definite integral by working out f(b) - f(a)
What do you get when you integrate a positive curve between two lines, x = a and x = b?
The area between the curve, the x-axis and the lines x = a and x = b.
What do you get if the area bounded by the curve and the x axis is below the x axis?
When you integrate it you get a negative answer.
How do you find the area between curves and lines?
- Work out your limits for the area required (eg.where do curves intersect or cut axes?)
- Integrate to find the area under the curve
- Find the area under the line (is it a triangle or trapezium?)
- Work out what you subtract to get to the area required