1. The function F is defined on [0, 10]. It is an antiderivative of g and satisfies F(7) = 0. Sketch a graph of F. 2. Use your knowledge of area to compute F(4). Explain your reasoning. 3. Write a formula for F using an appropriate integral of g. 4. The function G is defined on [0, 10]. It is an antiderivative of g and satisfies G(0) = –2. Sketch a graph of G. %3D 5. Compute G(3) and G(10). 6. Compare and contrast the graphs of F and G.

1. The function F is defined on [0, 10]. It is an antiderivative of g and satisfies F(7) = 0. Sketch a graph of F. 2. Use your knowledge of area to compute F(4). Explain your reasoning. 3. Write a formula for F using an appropriate integral of g. 4. The function G is defined on [0, 10]. It is an antiderivative of g and satisfies G(0) = –2. Sketch a graph of G. %3D 5. Compute G(3) and G(10). 6. Compare and contrast the graphs of F and G.

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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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

1. The function F is defined on [0, 10]. It is an antiderivative of g and satisfies F(7) = 0.
Sketch a graph of F.
2. Use your knowledge of area to compute F(4). Explain your reasoning.
3. Write a formula for F using an appropriate integral of g.
4. The function G is defined on [0, 10]. It is an antiderivative of g and satisfies G(0) = -2.
Sketch a graph of G.
5. Compute G(3) and G(10).
6. Compare and contrast the graphs of F and G.

Consider the graph of the function g shown below. The domain of g is [0, 10], and the
graph of g is comprised of two line segments and a quarter circle.
7
4
3
1
2
3
4
7
10
00

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