Calculus Integrals discussion and excercise problems

User Generated

Puneyrfruw

Mathematics

Description

Watch: http://www.youtube.com/watch?v=OLPl0wR85ho&feature=channel and/or

view: http://www.calculusapplets.com/fundtheorem.html

Discussion: 75 to 150 Words:  The first part of the Fundamental Theorem of Calculus addresses indefinite integrals. Explain how this is of practical benefit in regards checking whether you have correctly calculated an antiderivative. Give an example of this.

Explain how the second part of the Fundamental Theorem is of practical benefit in regards to finding a definite integral. Give an example.

Week 1 Assignment.docx

Unformatted Attachment Preview

You must show your work. No copying from a solutions manual. 6.1 Show that the function F(x) is an antiderivative of the function f(x) by differentiating F. 4. F(x) = ½ x^2 – 4x + e^2x – 1 f(x) = x – 4 + 2e^2x Find the indefinite integrals. 2 3 14. ∫ 𝑑𝑥 20. ∫(𝑒 𝑡 + 𝑡)𝑑𝑡 3 𝑥 24. ∫ (9𝑥 − − 1 ) 𝑑𝑥 √𝑥 Perform the indicated multiplication and then integrate. 38. ∫√𝑦(4 − 3𝑦 − 2𝑦 2 )𝑑𝑦 Simplify the indicated quotient and then integrate. 42. ∫ 5𝑥 2 −2𝑥+3 𝑑𝑥 √𝑥 6.2 Use the technique of substitution to perform each integration. 2. ∫(𝑦 − 6)3 𝑑𝑦 1 6. ∫ 𝑥−11 𝑑𝑥 14. ∫(3𝑦 − 2)2 𝑑𝑦 3 20. ∫ 𝑦 2 𝑒 −2𝑦 𝑑𝑦 𝑒𝑡 26. ∫ 𝑒 𝑡 −1 𝑑𝑡 6.3 Find the Riemann sum 𝑆𝑛 for the given function, interval, and value of n. 4. 𝑓(𝑥) = 9 − 𝑥 2 ; [𝑎, 𝑏] = [−3, 2]; 𝑛 = 5; 𝑐1 = −2.5, 𝑐2 = −1.5, 𝑐3 = −0.5, 𝑐4 = 0.5, 𝑐5 = 1.5 Evaluate each definite integral. 41 8. ∫1 𝑥 𝑑𝑥 4 14. ∫2 (7𝑥 + 2)𝑑𝑥 3 18. ∫2 (𝑥 2 + 2𝑥 − 4)𝑑𝑥 3 22. ∫1 2𝑒 −1.5𝑥 𝑑𝑥
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer


Anonymous
Just what I was looking for! Super helpful.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags