Find the integration inner product on C[-3,3] of the given functions. f(x) = 16x g(x) = 3x² (f, g) Ex: 5 :

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A: We have to find out the operation

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A: Given: The rule, 23f-2,-1+4f-2,0+f-2,1+f2,-1+4f2,0+f2,1 is applied to solve ∫-11∫-22fx,ydxdy.   To…

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A: Here we have, I=∫01x+1x2+2x2dx

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A: The answer is π/3.

Q: Find the integration inner product on C[-4, 2] of the given functions. f(x) = 20x g(x) = 3x3 %3|…

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Q: ) Evaluate (3t+ 5) cos dt using integration by parts. 4.

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A: As the given equation is an first order differential equation ,we can find integrating factor.

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A: We will solve the problem

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A: A detailed solution is given below

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A: SOLUTION-

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Q: 3. The integration of x e* with respect to x is: A. e2x. В. 2хе* С. 2

A: To integrate  xex2 with respect to x: ∫ xex2dx Apply u-substitution: u=x2 Differentiate both sides:…

Q: Find the integration inner product on C[–4, 1] of the given functions. f(x) = 15x g(z) = 3r* (f, 9)…

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Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: 7. Use integration by parts to prove that for any positive integer n, п - 1 Scos | cos"x dx = 1…

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Q: Which of the following can be evaluated directly by the Power Formula of Integration? Sx³ V25 – x4…

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Q: 1. Compute the given integral. Using Substitution Method 5x-12 dx = +C 5x2-24x-1 *

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Q: Find the integration inner product on C[-4, 3] of the given functions. f(x) = 16x g(x) = 2x?

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Q: v) ₁ √√¹-x² sin(x² + y²) dzdydx fő

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Q: Find the integration inner product on C[–4, 2] of the given functions. f(x) = 15x g(x) = 2x³ %3D…

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Q: 1 dy 3 yz-+ y7 = 1, when x = 0, y = 3 dx

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Q: Given f (x) = x – z² + 1 %3D - defined over the interval [0, 6]. Use integration methods to solve

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Q: Evaluate xsec¬xdx using integration by parts. OA x2 -sec-1x-(x² – 1)3/2+c 2 O B. x? 1/2 2 Oc x2…

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