Consider the following graph of f(x)=x² +1 (not to scale): y=x+1 Assume that the area under the curve from 0 to b is three times that of the area from 0 to a, that is, assume that f(x)dx = 3[* f(x)&x. a) What is the relationship between a and b? (Evaluate the integrals, leaving variables in your result.) b) Suppose that a = 1. Solve your equation from part (a) for b, both as an exact value and as a decimal approximation to 3 decimal places (with your calculator).

Q: Calculator OK. Consider the function f(x)=x' +4x+2 on the interval [0, 3). a. Find the AVERAGE VALUE…

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Q: A 27. Describe the geometric meaning of the double integral of a function of two variables.

A: To Describe the geometric meaning of the double integral of a function of two variables

Q: For the function, do the following. f(x) = 31 − 6x2  from  x = 1  to  x = 2   (a) Integrate ("by…

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Q: (8) Suppose m > 0. Find the coordinates of the points (in terms of m) where y = mx in- tersects y =…

A: Here we have to find the area.

Q: 1. Find the area between the curves of y = x2 +1 and y = x +7 from x = -2 to x = 3. Round to two…

A: Topic-application of integration

Q: 10. (8x + 3) dæ

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Q: Find the area of the region enclosed by y = 5 – x² and 9 = x2 – 3 as a definite integral (do NOT…

A: To Determine :-  The area of the region enclosed by y = 5 - x2 and y = x2 - 3 as a definite…

Q: 4. Let f(x) = x² – 9 and g(x) = 2x – 1. (a) Draw both functions on the same set of axes. (b) On your…

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Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. Enter…

A: Given:a = -3 b = 2f(x) = 3 + 5e0.8x  Solution:A=∫ab​f(x)dxA=∫−32​(3+5e0.8x)dx Evaluate the…

Q: 4.   please help me answer this question.

A: Step 1: Given two functions are: f(x)=x2, g(x)=15xwe have to find area enclosed between them. Step…

Q: Find the area between the curves (Hint: Your answer will be in terms of a.) The area is f(x)=x and…

A: area is=a3/6