6.4_Fundamental_Theorem_of_Calculus_summer

6.4_Fundamental_Theorem_of_Calculus_summer - Evaluate the...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
6.4 The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus: Let f be continuous on [a,b]. Then a b f(x) dx = F(b) – F(a) where F is any antiderivative of f, that is F’(x) = f(x). Geometric Interpretation of a Definite Integral a b f(x) dx = F(b) – F(a) Represents the “signed area” between the graph of f(x) and the x axis on the interval [a,b] That is: the area above the x axis minus the area below the x axis on the interval [a,b]. Find the exact area under the graph of f(x) =10 - x 2 on [-1,2] (56/3) Find the area under the graph of f(x)= -1/3x + 1 on the interval [1,3] (2/3)
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Find the area under the graph of f(x)= 4x 2 + 6x + 10 on the interval [1,7] (660) Evaluate the definite integral 2 21 52 dx (988) Evaluate the definite integral 0 1 (x 6 – 2x 2 + 1)dx Give answer as fraction (10/21)
Image of page 2
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Evaluate the definite integral ∫ 2 (x – 4) (x - 1 )dx Give answer as fraction (2/3) A company produces chairs. Management has calculated that the marginal cost function for producing x chairs is C’(x) = .0015x 2- .04x + 11 dollars/unit and x denotes the number of units. Fixed costs are 700 per day. What is the total cost of producing the 111 st through 220 th units/day. 110 ∫ 220 C’(x) = 5143 to nearest integer Evaluate the definite integral 1 ∫ 2 (6/x )dx 6ln(2) The velocity of the Sea Falcon II t seconds after firing a booster rocket is v(t) = -t 2 + 20 t + 440ft/sec, 0< t< 20. Find the distance covered by the boat over the 10 second period after the booster was activated. ∫ 10 v(t) = 15200/3 Evaluate the definite integral 1 ∫ 3 e x dx e 3- e...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern