Unit 6 – Fundamentals of Calculus Section 6

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Presentation transcript:

Unit 6 – Fundamentals of Calculus Section 6 Unit 6 – Fundamentals of Calculus Section 6.7 – The Definite Integral No Calculator

Fundamental Theorem of Calculus If f is continuous on [a, b] and F is any antiderivative on [a, b], then 36 20

15 10 6

Find the area under the curve from x = 0 to x = 1

Find the area under the curve from x = 1 to x = 2

Average Value of a Function on [a, b] Find the average value of on the interval [-2, 2]

Average Value of a Function on [a, b] Find the average value of on [-1, 1]

DIFFERENTIATE POSITION s(t) VELOCITY v(t) ACCELERATION a(t) INTEGRATE

Given on [0, 10], find the net distance traveled.

Given on [1, 2], find the net distance traveled.

Averages Average Value of a Function Average value of f(x) Average Rate of Change Average value of f ’(x)

Given on [2, 4]: a) Find b) Find the average position on the interval [2, 4] c) Find the average velocity on the interval [2, 4]

Given on [1, 3]: a) Find s(2) if s(0) = 3 b) Find the average acceleration c) Find the acceleration at t = 3

Given on [0, 4] with v(1) = 5 and s(0) = 2: a) Find s(1) b) Find the average acceleration.