x | 0 | 0.5 | 1.0 | 1.5 | 2.0 f(x) | 3 | 3 | 5 | 8 | 13 (5) A table of values for a continuous function is shown above. If four equal subintervals of [0,2] are used, which of the following is the trapezoidal approximation of ??² f(x)dx? (a) 8 (b) 12 (c) 16 (d) 24 (e) 32
Added by Nicholas K.
Close
Step 1
We are given a table of values for a continuous function and asked to approximate the integral of this function over the interval [0,2] using the trapezoidal rule. The interval is divided into four equal subintervals. Show more…
Show all steps
Your feedback will help us improve your experience
Qbs Educator and 79 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
12.) A table of values for a continuous function f is shown above. If four equal subintervals of [0,2] are used, which of the following is the trapezoidal approximation of ∫₀² f(x)dx? (A) 8 (B) 12 (C) 16 (D) 24 (E) 32 13.) What are all values of x for which the function f defined by f(x) = x³ + 3x² - 9x + 7 is increasing? (A) -3 < x < 1 (B) -1 < x < 1 (C) x < -3 or x > 1 (D) x < -1 or x > 3 (E) All real numbers 14.) Let f and g be differentiable functions with the following properties: (i) g(x) > 0 for all x (ii) f(0) = 1 If h(x) = f(x) * g(x) and h'(x) = f(x) * g'(x), then f(x) = (A) f'(x) (B) g(x) (C) eˣ (D) 0 (E) 1
Ma. Theresa A.
The table below gives data points for a continuous function f on [2, 10]. Using subdivisions [2, 5], [5, 8] and [8, 10], what is the trapezoid approximation of integral from 2 to 10 of f(x) dx? (A) 18 (B) 20 (C) 22 (D) 24 (E) 40
Israel H.
Use inequalities $(12),(13),$ and ( 14) to find a number $n$ of subintervals for (a) the midpoint approximation $M_{n},$ (b) the trapezoidal approximation $T_{n},$ and (c) Simpson's rule approximation $S_{n}$ to ensure that the absolute error will be less than the given value. $$ \text { Exercise } 5 ; 10^{-4} $$
PRINCIPLES OF INTEGRAL EVALUATION
Numerical Integration; Simpson’s Rule
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD