□ Use the definition of integral to prove that for = f'/h 1/x if X FO (x) is NOT if x=0 Riemann integral ble [0, 1]. (Hint: 200 £is divergent.)

Q: Evaluate (₁ F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

A: NOTE: Refresh your page if you can't see any equations. . C:=smooth curve form (-5,4) to (3,2)…

Q: Let ft)=F(t), where F (t) = 412– 5t²+ 5t¸ Evaluate the following integral using the Fundamental…

A: As we know from the fundamental theorem of calculus; If F't=ft then, ∫abftdt=Ftab=Fb-Fa   From the…

Q: Ss (2ava2 + 2) dæ dx r+1 vi) đt 64 Jo (sin 2x + cos 2x) dz

A: Firstly let's recall few basic integration formule.

Q: Suppose an object moves in space with the position functionr(t) = ⟨x(t), y(t), z(t)⟩ . Write the…

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Q: dydx tan x 1. 1+ y?

A: We will solve the following

Q: 4. Use the definition of the Riemann integral to evaluate f(x) dx where (a) f(x) = x². (b) f(x)= 3x…

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Q: x=3 Qs. A: Find * x²dx by using Riemann integral.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Express lim i odinflabai bas esinlob otatlavo noo T nousitedura oidd grian olderolm i=1 sin r;Ar as…

A: Answer: the evaluation of above integral is as shown below:

Q: The substitution u = r changes the integral 2xe²° dæ into 2ue%² du Select one: O True O False

A: Given that:                       1. Substitution of u=x3 in ∫012xex2dx into ∫012ue9u2du2. k≠0, then…

Q: QI/ Find the value of the line integral , F.dr when F-yi-xyj and C is the circular are in figure…

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Q: If m(E) = 0, show that any function f: E → Ris Lebesgue integrable and Se f = 0.

A: Given, mE=0 So, a measurable function f:E→ℝ is said to be Lebesgue integrable  (or simply inferable)…

Q: Use the Fundamental Theorem of Line Integrals to compute the work done F on an object that is moved…

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Q: 3. Evaluate the improper integral: dx | Tale + 1)'

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Use Greens Theorem to evalua te the line integral Sr -93 dx +x*dy. where C is the positively onented…

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Q: To create a saline solution, salt water with a concentration of 40 g/L is added at a rate of 500…

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Q: Evaluate the integral J x cot x² sin(in |sin x²l) dx.

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Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A: Line integral will be path independent if vector field whose integral we need  is conservative…

Q: dx ,2 /9 – x² 2

A: Solution

Q: 1 - dx x In x 2. Evaluate the improper integral or show that it is divergent.

A: To show that it is divergent.