Let f be a continuous function such that f changes from increasing to decreasing, and the graph of ƒ changes from concave up to concave down. Which of the following is true about themidpoint Riemann sum approximation for| f(x² + x)dxusing 4 subintervals of equal width?f(1²+1)+f(1.5ª +1.5)f(1.5° +1.5) +f(2ª +2)f(2° +2) + f(2.5² +2.5)f(2.5° +2.5) +f(3² +3)222Ais the midpoint Riemann sum approximation and underestimates f(x² + x)dx1( f(12+1)+f(1.5° +1.5)f(1.5° +1.5)+f(2² +2)f(2° +2) +f(2.5² + 2.5)f(2.5° +2.5) +f(3² +3)2Bis the midpoint Riemann sum approximation and overestimates| f(x² + x)d¤(f(1.252 + 1.25) + f(1.75² + 1.75) + f(2.25² + 2.25) + f(2.75² + 2.75)) is the midpoint Riemann sum approximation and underestimatesf(r² + x)dz(f(1.252 + 1.25) + f(1.75² + 1.75) + f(2.25² + 2.25) + f(2.75² + 2.75)) is the midpoint Riemann sum approximation. There is not enough information todetermine whether the approximation underestimates or overestimates2)dr.

Let the integral is given by, ∫abfx dx…

Let f be a continuous function such that f changes from increasing to decreasing, and the graph of f changes from concave up to concave down. Which of the following is true about the midpoint Riemann sum approximation for | f(x² + æ)dæusing 4 subintervals of equal width? f(1² +1)+f(1.5² + 1.5) f(1.5° + 1.5) + f(2² +2) F(2² + 2) + F(2.5² + 2.5) f(2.5° + 2.5) + f(3² +3) 2 A is the midpoint Riemann sum approximation and underestimates [ {(z² + z)dz f(1² +1)+f(1.5° + 1.5) f(1.5° +1.5) +f(2² +2) f(2ª + 2) + F(2.5ª + 2.5) f(2.5° + 2.5) + f(3² +3) 2 B is the midpoint Riemann sum approximation and overestimates c) (f(1.25² + 1.25) + f(1.75² + 1.75) + f(2.25² + 2.25) + f(2.75² +2.75)) is the midpoint Riemann sum approximation and underestimates (f(1.252 + 1.25) + ƒ(1.75² + 1.75) + f(2.25² + 2.25) + f(2.75² + 2.75)) is the midpoint Riemann sum approximation. There is not enough information to D determine whether the approximation underestimates or overestimates | $(2² + x)dz.

Let f be a continuous function such that f changes from increasing to decreasing, and the graph of f changes from concave up to concave down. Which of the following is true about the midpoint Riemann sum approximation for | f(x² + æ)dæusing 4 subintervals of equal width? f(1² +1)+f(1.5² + 1.5) f(1.5° + 1.5) + f(2² +2) F(2² + 2) + F(2.5² + 2.5) f(2.5° + 2.5) + f(3² +3) 2 A is the midpoint Riemann sum approximation and underestimates [ {(z² + z)dz f(1² +1)+f(1.5° + 1.5) f(1.5° +1.5) +f(2² +2) f(2ª + 2) + F(2.5ª + 2.5) f(2.5° + 2.5) + f(3² +3) 2 B is the midpoint Riemann sum approximation and overestimates c) (f(1.25² + 1.25) + f(1.75² + 1.75) + f(2.25² + 2.25) + f(2.75² +2.75)) is the midpoint Riemann sum approximation and underestimates (f(1.252 + 1.25) + ƒ(1.75² + 1.75) + f(2.25² + 2.25) + f(2.75² + 2.75)) is the midpoint Riemann sum approximation. There is not enough information to D determine whether the approximation underestimates or overestimates | $(2² + x)dz.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Question

Let f be a continuous function such that f changes from increasing to decreasing, and the graph of ƒ changes from concave up to concave down. Which of the following is true about the
midpoint Riemann sum approximation for
| f(x² + x)dxusing 4 subintervals of equal width?
f(1²+1)+f(1.5ª +1.5)
f(1.5° +1.5) +f(2ª +2)
f(2° +2) + f(2.5² +2.5)
f(2.5° +2.5) +f(3² +3)
2
2
2
A
is the midpoint Riemann sum approximation and underestimates f(x² + x)dx
1( f(12+1)+f(1.5° +1.5)
f(1.5° +1.5)+f(2² +2)
f(2° +2) +f(2.5² + 2.5)
f(2.5° +2.5) +f(3² +3)
2
B
is the midpoint Riemann sum approximation and overestimates
| f(x² + x)d¤
(f(1.252 + 1.25) + f(1.75² + 1.75) + f(2.25² + 2.25) + f(2.75² + 2.75)) is the midpoint Riemann sum approximation and underestimates
f(r² + x)dz
(f(1.252 + 1.25) + f(1.75² + 1.75) + f(2.25² + 2.25) + f(2.75² + 2.75)) is the midpoint Riemann sum approximation. There is not enough information to
determine whether the approximation underestimates or overestimates
2)dr.

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Question #3. Find convolution f * g when f = sint and g = t. Also verify that L{f} x £{g} = £{f*g}.
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