The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y = f(x) y 18 0 18 36 54 72 x (a) integral from 45 to 63 f(x) dx (b) integral from 0 to 81 f(x) dx
Added by Eduardo W.
Close
Step 1
Looking at the graph, this area is a triangle with base 27 (45 - 18) and height 18 (the value of f(x) at x = 45). The area of a triangle is 1/2 * base * height, so the value of the integral is 1/2 * 27 * 18 = 243. Show more…
Show all steps
Your feedback will help us improve your experience
Ma. Theresa Alin and 51 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
The graph of f is shown. Evaluate each integral by interpreting it in terms of areas: y = f(x) (a) ∫ from 0 to 16 f(x) dx (b) ∫ from 0 to 40 f(x) dx (c) ∫ from 40 to 56 f(x) dx (d) ∫ from 0 to 72 f(x) dx
Kyle S.
The graph of f is shown. Evaluate each integral by interpreting it in terms of areas: (a) ∫₀² f(x) dx (b) ∫₀⁵ f(x) dx (c) ∫₅⁷ f(x) dx (d) ∫₀⁹ f(x) dx
Andrew N.
The graph of $f$ is shown. Evaluate each integral by interpreting it in terms of areas. $\begin{array}{ll}{\text { (a) } \int_{0}^{2} f(x) d x} & {\text { (b) } \int_{0}^{5} f(x) d x} \\ {\text { (c) } \int_{5}^{7} f(x) d x} & {\text { (d) } \int_{0}^{9} f(x) d x}\end{array}$The graph of $f$ is shown. Evaluate each integral by interpreting it in terms of areas. $\begin{array}{ll}{\text { (a) } \int_{0}^{2} f(x) d x} & {\text { (b) } \int_{0}^{5} f(x) d x} \\ {\text { (c) } \int_{5}^{7} f(x) d x} & {\text { (d) } \int_{0}^{9} f(x) d x}\end{array}$
INTEGRALS
The Definite Integral
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD