The definition of the Definite Integral is ?_a^b f(x)dx = lim_{n ? ?} ?_{i=1}^n f(x_i)?x Interpreting this definition geometrically: • ?x represents __________________________________________________ • f(x_i) represents __________________________________________________ • f(x_i)?x represents __________________________________________________ • ?_{i=1}^n f(x_i)?x represents __________________________________________________ • Why do we take the limit of the expression? __________________________________________________
Added by Shelley D.
Close
Step 1
** Show more…
Show all steps
Your feedback will help us improve your experience
Ahmet Yavas and 97 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
Explain why the following integral is improper and then evaluate the integral. Why is this integral improper? A. One or both limits of integration are infinite. B. The integrand becomes infinite at some point in the interval of integration. C. The integrand is discontinuous at some point in the interval of integration. D. The integrand is undefined at some point inside the interval of integration. (Type an exact answer.)
Zhumagali S.
Explain why each of the following integrals is improper.
Ma. Theresa A.
Limits of sums Use the definition of the definite integral to evaluate the following definite integrals. Use right Riemann sums and Theorem 5.1 $$\int_{0}^{2}\left(x^{2}-1\right) d x$$
Integration
Definite Integrals
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