Lesson 18 Finding Definite and Indefinite Integrals

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Presentation transcript:

Lesson 18 Finding Definite and Indefinite Integrals MATH 1314 Lesson 18 Finding Definite and Indefinite Integrals

Geogebra Commands integral(f(x)) CAUTION: this command will not give the +C at the end of the integration. You must add that yourself!

Popper 21: The reverse of a derivative is the: antiderivative b. integral c. indefinite integral d. all of these 2. When taking an indefinite integral, a constant should always be added at the end. a. Always b. Sometimes c. Never The derivative of a function is f’(x) = 6x – 3. The function could be: a. 3x2 – 3x + 5 b. 3x2 – 3x + 2 c. 3x2 – 3x d. All are possible

Popper 21…continued Find the antiderivatives of the following: 4. f(x) = 2x3 + 4x – 6 5. 𝑓 𝑥 = 7 𝑥 3 + 2x 6. f(x) = 2x e5x2 a. F(x) = x2 – 7/(2x2) b. F(x) = x2 + e5x2 c. F(x) = 0.5x4 + 2x2 -6x + C d. F(x) = 0.2 e5x2

Basic Rules

Popper 22: A constant of integration should be added to the following: indefinite integrals b. definite integrals c. all integrals 2. Definite integrals have what as their answers: functions b. numbers c. depends on what is integrated 3. Complete the following: 𝑎 𝑏 𝑓 𝑥 𝑑𝑥= a. F(x) + C b. f(b) – f(a) c. F(b) – F(a) d. F(a) – F(b)

Popper 22…continued Determine the following integrals: 4. 4 𝑥 2 +5𝑥+3 𝑑𝑥 5. 25𝜋𝑑𝑥 6. 0 2 𝑥 2 +3𝑥 𝑑𝑥 a. 25πx + C b. (4/3)x3 + (5/2)x2 + 3x + C c. 12.5π2 + C d. 8.667