Chapter 13 Intergration

Question 1

How do you integrate x^n?

Answer 1

If dy/dx = x^n, then y = 1/n+1 x^n+1 + c when x doesn’t equal -1

Question 2

How do you integrate kx^n?

Answer 2

If dy/dx = kx^n, then y = k/n+1 x^n+1 + c

Question 3

How do you integrate polynomials?

Answer 3

Apply the rule of integration separately to each term

Question 4

How do you find the constant of intergration?

Answer 4

• integrate the function
• substitute the values (x, y) of a point on the curve into the integrated function
• solve the equation to find c

Question 5

What is a definite integral?

Answer 5

The value of an integral between two limits

Question 6

What are the three stages when you work out a definite integral?

Answer 6

1. Write the definite integral statement with its limits, a and b
2. Integrate and write the integral in square brackets
3. Evaluate the definite integral by working out f(b) - f(a) (b is always the larger number)

Question 7

How do you calculate the area between a positive curve, the x-axis and the lines x=a and x=b?

Answer 7

Calculate the definite integral of f(x) between b and a

Question 8

What happens when the area bounded by a curve and the x-axis is below the x-axis?

Answer 8

The definite integral is a negative number