Integration

Question 1

How is the integral of a function f(x) written with respect to x?

Answer 1

You draw a tall ‘s’ shape and afterwards, ‘f(x)’ and then ‘dx’.

Question 2

How do you integrate a function?

Answer 2

For every term, ax^n (except ax^-1):
(ax^(n + 1)) / (n + 1)
Don’t forget to add c (a constant) at the end!!!!

Question 3

What do you do if there are lots of terms in a function?

Answer 3

integrate them separately.

Question 4

What do you get if you integrate the equation for the gradient of a curve?

Answer 4

The equation of the curve.

Question 5

What do you need to find the whole equation of a curve and why?

Answer 5

A point on the curve in order to find c.

Question 6

What is a definite integral?

Answer 6

Definite integrals have limits next to the integral sine. They tell you the range of x-values to integrate between.

Question 7

How do you find a definite integral?

Answer 7

Integrate the function as normal, but don’t add a constant of integration. Work out the value of the definite integral by putting in the limits and subtracting the lower limit from the higher one.

Question 8

What is the value of a definite integral?

Answer 8

The area between the x-axis and the graph of the function you’re integrating between the two limits.

Question 9

How do you find the area of a portion of a curve which is both below and above the x-axis?

Answer 9

Find the areas above and below the graph separately and add them up at the end.