Chapter 15: Introduction to Integration

Question 1

State the Riemann Integral, and the 3 ways that the Riemann Integral can be solved

Answer 1

Riemann Integral:
∫ ₐᵇ f(x) dx

Can be found:
1) Algebraically
2) GDC calculator page
3) GDC graphing page

Question 2

Explain antidifferentiation and find the antiderivative of a function
(Eg. dy/dx = x², y = ? )

Answer 2

Antidifferentiation:
- Finding y from dy/dx
- Finding f(x) from f’(x)

Eg. Antiderivative of x² is 1/3x³

∫ ₐᵇ f(x) dx = F(b) - F(a), when F(x) is the antiderivative of f(x)

Question 3

State the 6 rules of definite integrals

Answer 3

1) ∫ ₐᵃ f(x) dx = 0
2) ∫ ₐᵇ f(x) dx = - ∫ ₆ᵃ f(x) dx
3) ∫ ₐᵇ f(x) dx + ∫ ₆ᶜ f(x) dx = ∫ₐᶜ f(x) dx
4) ∫ ₐᵇ [f(x)+g(x)] dx = ∫ ₐᵇ [f(x) dx + ∫ ₐᵇ [g(x)
5) ∫ ₐᵇ k dx = k (b-a)
6) ∫ ₐᵇ k f(x) dx = k ∫ ₐᵇ [f(x) dx