Which of the following is always true for integrable functions fand g? A dx = dx B dr (c) , where g(x) #0 dx= (x) D dr

Q: If the change of variables u=x²+4 is used to evaluate the definite integral f(x) dx, what are the…

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Q: Find the Particular Integral for the given differential equatiorn d²y dy +3- dx +6y =2x²+x+5 dx2…

A: using expansion,         (1+x)-1 =1-x+x2 -x3+...

Q: The value of the definite integral' f(x )dx for f(x) = 3 is:

A: We are going to evaluate the value of the given definite integral for f(x)=3

Q: Find x" In x dx; n # -1, n real. (Use C for the constant of integration.)

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Q: If 9. 10 f(2)dæ = /: | F(2)dx - / f(x)dæ, f(x)dx + %3| 3 9, what are the bounds of integration for…

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Q: Find the integral | 2(x* – x°)(x5 – 1)®dx а. b. In x2 dx 2х J x + 3)* С. 5.

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Q: Suppose that f(x) has a continuous derivative, (T/2 f(-т/2) — 0, f(T/2) = T/4 and dx = 3. %3D 7/2…

A: Given that:

Q: Find the differential dy of the given function. (Use "dx" for dx.) = 8x3/4 dy = %3D

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Q: Q: Find the integration for the following functions: - 1.- °(1-cos2x) 2-5 2- sin(tnx) dx 3-f-…

A: According to the guidelines issued by the company we are supposed to answer only first three sub…

Q: d Prove In Jax| dx In x for any constant a. dx

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Q: find the critical points:

A: Given function is  and the interval isThe critical points of a function are obtained when the first…

Q: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

A: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

Q: Evaluate the integral. | (e7* +3e -x) dx 7X +3 e -X) dx=

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Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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Q: Evaluate the integral. dx 4 a > 0 (a² + x²)3/2?

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Q: 4 dx Vx(1 + x) roper for two reasons: The interval [0, co) is infinite and the integrand h 4 4 dx =…

A: Here we use substitution so simplify the integration.

Q: x-3 dx r³+9x +9.x

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Q: Evaluate the double integral 2. dy dx 3/x

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Q: Q3: a) Evaluate the following integrals: 1. f sin2x 1+ cos²x dx. √9-x2 2. fv-x² dx 3.f 1+x dx

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Q: Find the total derivative of the function f(x, y, z) =+z In (2x+1)+sin (xy) xz

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Q: If 9. 3. 6. f(x)dx = || f(x)dz + 6. what are the bounds of integration for the first integral?…

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Q: c) Suppose fand g are integrable and that S(x)dx = 4 , [ f(x)dx= 6 , [ g(x)dx= -2. Find the…

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Q: If the change of variables u = x + 1 is used to evaluate the definite integral f(x) dx, what are the…

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Q: 5. Suppose fand g are continuous functions and that: f(x)dx=-4, f(x) f(x)dx=6 and 8(x)dx=8 use the…

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Q: 79. What are the new limits of integration if we apply the substitution u = 3x +7 to the integral…

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Q: Which of the following is not an improper integra cos x dx 0. 1 dx cos x 0. cos x dx 0. 1 dx OUESTI…

A: Improper Integral  integrand is discontinuous at a point  in given limit

Q: Which of the following uses integration by parts? (1) fxcos.x°dx (3) fxlnxdx (2) [x'e*dx - In x dx…

A: we have to find the integration by parts from the following

Q: Evaluate the integral x3 dx 2+100 S x3 dx +100 (Use C as the arbitrary constant.)

A: Given,

Q: e ln (xle) (2– sec²r)cm#/c°sec³x sec(3A – x) What should be the value of A for -dx to be integrable…

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Q: Q1:Choose theappropriate value to integrate the following sin(In x) dx (sin (In x) – scos (In x)) +…

A: Solution I=∫sinin x dx        Let  lnx=t⇒x=et         1x dx=dt          dx=xdt…

Q: 5. Find the indefinite integral. A) f dx (x-3)Vx -6x+5

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Q: (2– sec²x) ln (# /e)scc³x sec(3A – x) What should be the value of A for to be integrable using the…

A: Let's find.

Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x*-1sin x…

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Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

Q: evaluate the given integral.

A: Solution:-The given integral is  ∫x+2(x-1)(x+3)dx since  x+2(x-1)(x+3) is solved by partial…

Q: Evaluate the integral 1 2-x xy dy dx 0 x2

A: Here we have to evaluate the given integral

Q: The approximation of the integral f(x-1) cos(x+2) dx using two points Gaussian quadrature formula…

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Q: (a) Evaluate the integral [x (x* -1) ´dx by using substitution.

A: To evaluate the given integral ∫x3x4-12 dx by using substitution.

Q: b. d. 1 dx x4 ° 1 dx f. | h. (y³ – 3y²) - 8

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Q: (b) Approximate the definite integral f"/² cos(x)dx by employing the Composed Midpoint rule with n =…

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Q: a) Find the integral 3x7 dx dy . Vr – x2 -

A: Given, the integral is Here y = 0 and y = 1 and x = Öy and x = y2.

Q: -3 evaluate the integral (x2 – x + 2) dx using its definition.

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Q: ग Use the Midpoint Rule to evaluate the integral fx sin(x)dx. D]2 co | Fo 프2 NN

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Q: 3 Suppose that f(x) dx = 7, | f(x) dx = 5, and | f(x) dx = 10. %3D Evaluate the following definite…

A: (a) The given integral is: I=∫35f(x)dx As we know from the integral theorem,…

Q: s the indefinite integral | x2 cos(x3) dx becomes 1 cos(u) du- must also convert the integral…

A: Given query is to find the integral limits.

Q: Use the Error Bound to find the least possible value of N for which Error (SN) <1 x 10 9 in…

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Q: 1. Integrate by parts and evaluate x cOS x dx 0, а. b. In(x²) dx 1 In x dx x5 С.

A: By using Integration by part  ∫udv=uv−∫vdu

Q: If f is continuous and ∫90 f(x)dx=4  find the following integral. ∫30 xf (x2)dx

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