Integration 2

Question 1

How do you find the area between a curve and the 𝑥-axis?

Answer 1

The equation area bounded by a curve 𝑦 = 𝑓(𝑥), the 𝑥-axis, and the lines 𝑥 = 1 and 𝑥 = 3 is given by:

𝐴𝑟𝑒𝑎 = ₁∫ ³𝑓(𝑥) 𝑑𝑥

Question 2

How do you find the area under the 𝑥-axis?

And what should you do to find areas above and below the x-axis?

Answer 2

When the area is below the 𝑥-axis it will give a negative value. You must formally dismiss this negative to leave the positive value as your area.

If there are areas both above and below the 𝑥-axis to find, work out each area separately and add their positive values together.

Question 3

How do you find the area between a line and a curve?

Answer 3

The area between a line and curve is found by using both integration and areas of shapes created by the line and the limits. Look for shapes such as triangles, rectangles and trapezia.

You may also find the area between a line and a curve by subtracting the function that is below the other from the other function, then integrating the result of this between the appropriate limits.