If S f(x) dx = 12 and f(x) dx = 42, find the value of (2f(x) – 3) dx. 1.

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Q: (c) J xe0.4x (0.4x + 1)2 d dx

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Q: Find f(x) dx = -3.5 -3.5 and 2f(x) – 3 dx = -1

A: Given: ∫-61.5fx=2∫-6-3.5fx=3∫-11.5fx=4

Q: (e + x + 2)dx 3.

A: The sum rule for integration states that ∫fx+gxdx=∫fxdx+∫gxdx. The integration formula for…

Q: 9. If | f(x) dx = 20 and f(x) dx = 3.6, find f(x) dx.

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Q: y(x*-lIng) clx + xdy =o

A: The given equation is, y(x2+lny)dx+x dy=0

Q: Given f(x) dx = 0 and f(x) dx = 7, evaluate (a) F(x) dx. (b) F(x) dx - f(x) dx. 4f(x) dx. (d) 4f(x)…

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Q: Suppose Find the value of f(82). f(82) = dx f(x) = 10, f(0) = 22.

A: I am attaching image so that you understand each and every step.

Q: Solve (x – y)dx + xdy = 0.

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Q: Given 11 1(² f(x) dx = 3 and 10 f(x) dx = -3, find 10 f(x)dx.

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Q: Given f(x) dx = 13 and f(x) dx = 5, evaluate %3D (a) f(x) dx. (b) f(x) dx. (c) r(x) dx. (d) 3f(x)…

A: Given ∫05fxdx=13 and ∫57fxdx=5 Solution for a: Note that ∫acfxdx=∫abfxdx+∫bcfxdx Therefore,…

Q: Given f(x) dx = 12 and f(x) dx = 5, evaluate (a) f(x) dx. (b) f(x) dx. (c) f(x) dx. (d) 2f(x) dx.

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Q: '3. 9. Given fx) dx = 4 and f(x) dx = -1, evaluate the following. 9. (a) f(x) dx (b) f(x) dx 3 (c)…

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Q: If fſ f (x)dx = 8, what would f f(x)dx equal?

A: Given, the definite integral gives result 8. Concept - when the limits of integration is changed…

Q: 2e2x) when x=0 and y=3. dx Compute

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Q: Find the value of +5 f(x) is odd, and ₂ f(x) dx = 5 -5 √₂ f(x) dx = f(x) dx, given than

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Q: (b) Given [f(x)dx = 21 f (x)dx = 29, find the value of S. 25 (x)dx . and

A: ∫102f(x)dx=21∫107f(x)dx=29

Q: Suppose Find the value of f(10). f(10) = _. d _ƒ(x) = 6x, f(1) = 8. dx

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Q: Suppose f(x) dx 16 and f(x) dx = 10. | f(x) dx = Then %3D

A: topic - definite integral

Q: Ho Find (yor dy d'y ) and (y or -) for the following functions: dx dx L 2. y= x² (x-1)² 5. y=(x²…

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Q: dy Solve the equation x = x2 + 3y dx

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Q: SSx = 172.5, SSY = 80.6, and ∑[(X – Mx) (Y – MY)] = 95.33, r =  A. .08. B. .01 C. –.81. D. .81.

A: SSx = 172.5 SSY = 80.6 and ∑[(X – Mx) (Y – MY)] = 95.33

Q: IF f(x) = 13sin(x)-8e*. Calculate: df(x) dx =

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Q: (#9) S x2 dx V16-x²

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Q: f(x) dx =1 then the value of If f(3x +1) dx is %3D ! 1

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Q: Given f(x) dx = 0 and f(x) dx = 9, evaluate (a) f(x) (b) f(x) dx - f(x) dx. 1 (c) 3f(x) dx. 1 (d)…

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Q: Find the values of a and b such that a = b + [¹ f(x) dx − [*f(x) dx = f*f(x) dx. - 11

A: Given,

Q: dx Evaluate -1 x2 - 0 -2

A: The integration formula is ∫xndx=xn+1n+1+C.

Q: Use the property | f(x)dx f(x)dx to show that f(x)dx = 0. = 9. By the given property, f(x)dx - |…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.