Calculus CALCULUS Ideas from C3 you may need to know: –differentiation: the product rule –the quotient rule (in formula book) –chain rule, e.g. differentiate.

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Presentation transcript:

Calculus CALCULUS Ideas from C3 you may need to know: –differentiation: the product rule –the quotient rule (in formula book) –chain rule, e.g. differentiate –implicit differentiation –integration: by substitution –by parts (in formula book)

Calculus Differentiation and integration of trig functions, including powers of sine and cosine: Not in the formula book

Calculus Differentiation of inverse trig functions Formula Book:

Calculus Integration using inverse trig functions Formula Book: Use a big algebra stick to batter your function into one of these standard forms

Calculus Examples

Calculus

Don’t forget to use radians if there are limits Sometimes you might have to use a nasty trig substitution. You might have to complete the square before substituting Don’t forget integration by parts, e.g. how would you integrate arctan x?

More examples Evaluate a) b) a) b)

More examples Evaluate c) c) In these cases we use integration by substitution.

More examples Evaluate d) c) In these cases we use integration by substitution.

Example Find Integrals of the form or Rearranging the denominator so we have something +1 gives let x – 1 = u

Example Find More examples