I am unsure about how to solve the attached fundamental theorem question. ### Graph of the Function \( g(x) \)The image displays a graph of the function \( y = g(x) \). The graph is plotted on a coordinate grid and shows a curve that starts at the point (0, 4), decreases to a minimum around x = 4, and then increases towards the right beyond x = 7.### Evaluate the IntegralsThe following integrals are evaluated by interpreting them as the areas under the curve:(a) \(\int_{0}^{2} g(x) \, dx = 4\)- The integral from 0 to 2 of \( g(x) \) represents the area under the curve between x = 0 and x = 2, shaded in green.(b) \(\int_{2}^{6} g(x) \, dx = 6.285\)- The integral from 2 to 6 of \( g(x) \) represents the area under the curve between x = 2 and x = 6, shaded in red.(c) \(\int_{0}^{7} g(x) \, dx = \frac{1}{2}\)- The integral from 0 to 7 of \( g(x) \) represents the area under the curve between x = 0 and x = 7, shaded in red.

NOTE: Refresh your page if you can't see any equations. . the base of the triangle is 2 and the…

Answered: Consider the graph of the function…

Consider the graph of the function g(x): yA 4 y=g(x) 2- 4 Evaluate the following integrals by interpreting them in terms of areas (а) g(x) dæ =[4 (b) , 9(x) dx =[6285 7 (c) g(x) dx = 1/2

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

I am unsure about how to solve the attached fundamental theorem question.

### Graph of the Function \( g(x) \)

The image displays a graph of the function \( y = g(x) \). The graph is plotted on a coordinate grid and shows a curve that starts at the point (0, 4), decreases to a minimum around x = 4, and then increases towards the right beyond x = 7.

### Evaluate the Integrals

The following integrals are evaluated by interpreting them as the areas under the curve:

(a) \(\int_{0}^{2} g(x) \, dx = 4\)

- The integral from 0 to 2 of \( g(x) \) represents the area under the curve between x = 0 and x = 2, shaded in green.

(b) \(\int_{2}^{6} g(x) \, dx = 6.285\)

- The integral from 2 to 6 of \( g(x) \) represents the area under the curve between x = 2 and x = 6, shaded in red.

(c) \(\int_{0}^{7} g(x) \, dx = \frac{1}{2}\)

- The integral from 0 to 7 of \( g(x) \) represents the area under the curve between x = 0 and x = 7, shaded in red.

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