Chapter 13 - Integration Flashcards

1
Q

What do you get when you integrate xn?

A

1 xn + 1 + c

n + 1

Add a power to x and divide by the new power

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2
Q

What do you get when you integrate kxn?

A

k xn + 1 + c

n + 1

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

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3
Q

How do you integrate polynomials?

A

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

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4
Q

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

A

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

ie. integrate each function separately in turn.

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5
Q

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

A
  • 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
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6
Q

How do you calculate the definite integral?

A
  • Integrate the function
  • Write the integrated function in square brackets [f(x)]ba
  • Evaluate f(b) - f(a)
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7
Q

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

A
  • 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)
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8
Q

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

A

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

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9
Q

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

A

When you integrate it you get a negative answer.

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10
Q

How do you find the area between curves and lines?

A
  • 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
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