Let f be a continuous function such that | f(x) dx = -10 and | f(x) dx = 9. What is the value of (f(z) + 3) dx? -2

Q: Let f be a continuous function such that f(x) dx: = -1 and f(x) dx = = 9. %3D 2 2 | f(x) dæ? What is…

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Q: Suppose that f and g are continuous functions such that 3 | f (2) f (x) dæ = 2 and | [2f (2) + g (x)…

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Q: 9. If f is continuous and f(x) dx = 2, find f(2x) dx.

A: Given,  ∫06 fx  dx=2

Q: If f is continuous and f(x) dx = -1, find f(2x) dx.

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Q: 10 If f is a continuous function and F'(x)=f(x) for all x € R, then x)dx=?

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Q: B-Test and proof the function So (x In x)² dx

A: ∫01(x logx)2dx=∫01x2 (log x)2dx use integral by parts, ∫udv=uv-∫vdu u=(logx)2…

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (4, * ).…

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Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the…

A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at…

Q: Let f be a continuous function such that -6 [', f(x) dx = 9. What is the value of -3 f(x) dx = -10…

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Q: 9. If f(5) = 10, f ' is continuous, and f '(x) dx = 15 18, what is the value of f(6)? %3D f(6) =

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Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and g(2x)dx = 3. %3D 2 Find æg(3x²)dx.

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Q: Let f(x) = 3x+ 4x. Evaluate dy when x=2 and dx=0.1

A: Given that fx=3x2+4x To evaluate dy when x = 2 and dx = 0.1.

Q: 64 8. f(x) dx = 14, find xf(x?) dx. If f is continuous and %3D

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Q: 67. If f is continuous and f(x) dx = 10, find f(2x) dx

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Q: 3 f(x) dx = 4, find | xf(x*) dx. If f is continuous and

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Q: Let f be a continuous function such that f(x) dx = –3 and -8 7 | f(x) dx = -2. What is the value of…

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Q: If f is continuous and f(x)dx=4, | xf(x?)dx=

A: We will find the value of the integral as following.

Q: Suppose that f(1) = 1, f(4) = 6, f (1) = 7, f '(4) = 5, and f " is continuous. Find the value of xf…

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Q: et f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

A: Let f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

Q: Let f be a continuous function such that | f(x) da = 13 and 10 3 f(x) dx = 8. What is the value of…

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Q: Suppose that a continuous function g satisfies: g(x)dr = 30 and g(2x)dx = 3. 0. 2 Find r9(3x²)dx.

A: Suppose that a continuous function g satisfies: ∫03gxdx=30 and ∫06g2xdx=3. The, we have to find the…

Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: The sketch that represents a continuous function, y = f(x), such that: f'(-3)=Ø f(-3) = 5 and A(1) =…

A: The graph of continuous function f(x) is given in the options. The given data of the function f(x)…

Q: If f (x) and g(x) are continuous functions, then S(x) + g(x)] dx = | g(x)dx+ f(x)dx.

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Q: '49 If f is continuous and f(x) dx = 18, find | xf(x?) dx.

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Q: Let f be a continuous function such that | f(x) dæ = 5 and f(x) dx = 3. %3D | 4f(æ) dæ? What is the…

A: Recall: Properties of integral:  i)   ∫abf(x)dx=-∫baf(x)dxii) ∫abf(x)dx+∫bcf(x)dx=∫acf(x)dxiii)…

Q: If f is continuous and f(x)dx=4, xf(x2)dx=

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Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

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Q: 3 Let f(x) = 8x° 1 df 15x - 5, x2 1.5. Find the value of dx at the point x= 2004 = f(7). %3D

A: Known fact: derivative of f-1x=1f' f-1x.

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

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Q: (c) Does there necessarily exist a differentiable function h with 0 < h(x) <1 and E = {x : h(x) = 0}…

A: Sol:in the given question we have to tell about the differentiable function f(x)s.t whose range is…

Q: Let f be a continuous function such that f (x) dx 5 and 6° | f(x) dx = 3. What is the value of |…

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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Q: Let f be a continuous function such that 10 9 f(x) dx = 5. What is the value of f(x) dx = -6 and…

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Q: 87. If f is continuous and f(x) dx 10, find f(2.x) dx. %3D

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Q: Suppose that f(a) = f(b) = 0 and the second derivatives of f exist on the closed interval [a, b].…

A: Prove that ∫abx-ax-bf"xdx=2∫abfxdx.

Q: Let f and g be continuous functions. If Sz f (x) dx = 6 and f g (x) dx = 10, then f3 (5f (x) +g (x))…

A: Use property of definite integration

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

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Q: Let f be a continuous function such that 2 Lª¸ ƒ(2) dx = - f(x) dx = -8. What is the value of -3 2…

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Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4

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Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

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Q: Let f be a continuous function such that 10 1 of f(x) dx? 4 What is the value of 4 8 f(x) dx 10 1²°…

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Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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Q: 3 xf(x2)dx df(x) dx = -9, find If f is continuous and 0

A: f(x) is continuous

Q: What is the continuous extension of f(x) = at point x-1. x -1 x2-1' %3D x +x-2 find dy dx

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Q: Let f be a continuous function such that f (x) dx = -4 and 1 f(x) dx = –14. What is the value of 2…

A: As we know that;  The properties of the definite integral; 1). ∫abfxdx=-∫bafxdx…

Q: Draw the graph of a continuous function f(x) where f(-2) = 0, f(2) = 0, but there is no value c€…

A: Given: f(-2)=0 ;     f(2)=0but there exists at least one c∈-2, 2…

Q: sin(bx) x0. Find a value of b such that f is continuous, or explain why no such value exists.

A: Given, f(x)=sin(bx)xx&lt;0exp(x+5)x≥0

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.