Chapter 13 - Integration

Question 1

What do you get when you integrate xⁿ?

Answer 1

1 x^{n + 1} + c

n + 1

Add a power to x and divide by the new power

Question 2

What do you get when you integrate kxⁿ?

Answer 2

k x^{n + 1} + c

n + 1

Add 1 to the power of x and divide by that new power.

Question 3

How do you integrate polynomials?

Answer 3

Apply the rules of integration separately to each term (expand and simplify first if needed to get into a polynomial format)

Question 4

What do you get when you integrate (f’(x) +/- g’(x))?

Answer 4

f(x) +/- g(x) + c

ie. integrate each function separately in turn.

Question 5

How do you find the constant of integration (“c”) ?

Answer 5

• 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

Question 6

How do you calculate the definite integral?

Answer 6

• Integrate the function
• Write the integrated function in square brackets [f(x)]^b_a
• Evaluate f(b) - f(a)

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

• 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)

Question 8

What do you get when you integrate a positive curve between two lines, x = a and x = b?

Answer 8

The area between the curve, the x-axis and the lines x = a and x = b.

Question 9

What do you get if the area bounded by the curve and the x axis is below the x axis?

Answer 9

When you integrate it you get a negative answer.

Question 10

How do you find the area between curves and lines?

Answer 10

• 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