By the contour integration, show that: 0 dx = 3π (x² + a²)3 16a5 a>0

Q: dx (x+1)Vx²+2x

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Q: Find the da/dx, where a is a function of x: a²x² + 2ax = a.

A: The given function,        a2x2+2ax=a

Q: Rewrite the integration in terms of u. 2x dx = du x² + 16

A: Given :∫032xx2+16dx

Q: Given y = x³ 11 Bac 2³/27x² + 2x, find dy dx H Use the math type b

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Q: Bonus : Show: b. f(x+c) dx fcxdx %3D ate

A: According to the Fundamental Theorem of Calculus,

Q: In question (c), please use the computed result to explain why Dx=c is inconsistent

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Q: Show that the value of Vx + 8 dx lies between 2V2 - 2.8 and 3.

A: According to the question, we have to prove that the value of integral ∫01x+8 dx lies between 2.8…

Q: Find I using integration or geometry: I = 5 dx dy .

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: d²x dt² - x=0, x(0)=0, x(1) = 1

A: We have to find the solution of the differential equation.

Q: Find the dy/dx y=2log(9x+16)

A: ddxlog x = 1x

Q: Find d dx x3 Stan(t² + 5)dt.

A: I have explained everything with in the solution. Please go through that.

Q: Find the integration Sx cos 2x dx

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Q: Show that: (e) (VF) = 1 dx

A: Derivative of a function xn: ddxxn=nxn-1                               (1) Given function is: f(x)=x…

Q: For the function y = x² + 2x, the value of dy when *=3 and dx=0.1 js -0.15 A) 0.15 B) C) - 0.8 0.8…

A: We will find out the required value.

Q: d d (F(x³)) dx dt dx 14 ..

A: (1).   The given expression is: ddxFx3=ddx∫14x3 e-t2 dt

Q: dx S x(1+(lnx))²) 2.

A: This question is related to indefinite integration, we will solve it using given information.

Q: Integrate: S dx 5+ x2 5x

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Q: Approximate / 1+r² dr using four rectangles and the left endpoint method (L4).

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Q: Use n = 6 subdivisions to approximate the value of Vx +2 dx by the trapezoidal rule.

A: The given integral is ∫06x+2dx and the value of n is 6. Using the trapezoidal rule, approximate the…

Q: x2 dx V4 – x2

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Q: 3 y = Vlog2(sin5 x)

A: Given equation is y=log2sin5x3

Q: (x² - 4) dx x² + 2x² + 2x S

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Q: Integrate each of the following. Show complete solution. 1. 1000dx 2. S²x¹ + 3x² + 1)dx 3. f(u² + u…

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Q: ) Use implicit differentiation: + x²y +4y? = 6 %3D

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Q: Find: f 4t Vi + dt =

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Q: dx 2х -3 2)

A: Given integration is :   To find the value of integration.