1. a) Find the area of the region lying between $f(x) = x^2 - 3x + 2$ and x - axis between $x = 2$ and $x = 4$ by the limit definition. 1. b) Check your answer in a) by finding a definite integral.
Added by Ashley C.
Close
Step 1
Step 1: The area of the region lying between $f(x) = x^2 - 3x + 2$ and the x-axis between $x = 2$ and $x = 4$ is given by the definite integral: $$A = \int_2^4 (x^2 - 3x + 2) dx$$ Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 58 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
2) Find the area as the limit of a sum for the region between the functions f(x)= -x^2+3x and y= 0.
Adi S.
Vincenzo Z.
Section 4.1 4.4 4.5: Problem 6 Definition: The AREA A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles. A = lim R, lim [f(x1)Ax + f(x)Ax + tf(x)Ax] Use the above definition to determine which of the following expressions represents the area under the graph of f(x) = x^2 from x = 0 to x = 2. A. lim (n→∑) [f(xn*)Δx] (where Δx = 2/n, xn* is any point in the interval [x_(i-1), xi]) B. lim (n→∑) [f(xn*)Δx] (where Δx = 2/n, xn* is the right endpoint of the interval [x_(i-1), xi]) C. lim (n→∑) [f(xn*)Δx] (where Δx = 2/n, xn* is the midpoint of the interval [x_(i-1), xi]) D. lim (n→∑) [f(xn*)Δx] (where Δx = 2/n, xn* is the left endpoint of the interval [x_(i-1), xi]) (b) Evaluate the limit that is the correct answer to part (a). You may find the following formula helpful: (1 + 2 + 3 + ... + n) = n(n + 1)/2 Value of limit
Sri K.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD