Chapter 13 Integration - Year 1

Question 1

How so you integrate?

Answer 1

You increase the power by 1 and divide by the new power (or X by the reciprocal)

Question 2

What does f’(x) integrate to?

Answer 2

f(x)

Question 3

How do you find the equation if a line if you are given a point that it passes through and the gradient function?

Answer 3

You integrate the gradient function and then substitute the y and x value in to find what c is

Then rewrite the full equation out

Question 4

What is a definite integral calculating?

Answer 4

The area between the x axis and the line

Question 5

What do you need to remember to add on the end of all integrals?

Answer 5

+C

Question 6

What is vital with integrals?

Answer 6

+C

Question 7

When finding the area under a curve what do you need to be careful about? Why?

Answer 7

1) if the area is underneath the graph you will get negative area. So you just take the module of that (positive value)

2) if the graph switches from + to - area within the limits of the integrals then you will get the wrong answer as the calculation will give you the + area - the - area as a final calculation. You need to find where it cuts the x axis and do 2 separate integrals

Question 8

What should you always do to avoid a silly mistake?

Answer 8

Draw the graph

Question 9

How do you find the area between two lines?

Answer 9

Sketch them first

Then you do the integral of both and then subtract one from another

Question 10

What is the special case with finding the area between 2 lines?

Answer 10

If the top line is f(x) and the bottom line is g(x) you can do the integral of f(x)-g(x).dx