46. Bound on an integral Let f be a continuously differentiable function on [a, b] satisfying " f(x) dr = 0. a. If c = (a + b)/2, show that (x - c)f(x)dx. xf(x)dx = (x - c)f(x)dx + = |x – c| and e = (b – a)/2. Show that (f(c + t) - f(c - 1)) dt. xf(x)dx = c. Apply the Mean Value Theorem from Section 4.2 to part (b) to prove that (b – a) -M, 12 f(x) dx s where M is the absolute maximum of f' on [a, b].

Q: 5. (a) Use integration by parts to find f xe-3x dx. +00 -3x (b) Determine whether the improper…

A:

Q: Find a function f € span(1, cos x, sin x) which minimizes the integral 2πT √²* |x +1 − f(x)| ²dx.

A: Given a function                     f∈span1, cosx, sinx

Q: how I calculate the definate integral 3x^2-e^2x(dx) on the interval ln3 to 0

A: To find the definite integral

Q: Evaluate the definite integral S (1+ 2x) dx using Riemann sum.

A:

Q: 2.fe-2y dy

A:

Q: In(x) Differentiate the function F(x) = | cos(e') dt %3| 1/r Show and justify your work. (Hint:…

A:

Q: (5) Find the indefinite integral (a)f Vtan x sec²dx (b)fem2* sec² 2xdx sin x (c) Cos x 1 cos-do 0 2

A:

Q: Evaluate the integral. (Use C for the constant of integration.) √x²√3 dx √3+2x-x²

A:

Q: Verify directly from (3) that the solution has derivatives of all orders in {z > 0}. Asume that h(x,…

A: Sol

Q: mcory amu LAampIOS 45. Finding an upper limit of an iterated integral Solve for a: 1-x² ¢4-x²-y 4 dz…

A:

Q: Determine | An (x) An+1(x) dx, from the relation: tn .1 Σ (2n + 1)! tn+1 A, (x) An+1(x) dx n=0 n -1

A:

Q: 113. Suppose that F(x) is an antiderivative of f(x) = (sin x)/x, x > 0. Express sin 2x dx х in erms…

A:

Q: 17. Consider f(x) = dt. DO NOT state that f(x) = In x but explain how it behaves exactly like the…

A: In the question we need to evaluate the integral.

Q: x³ + 6x2 + x+2 2 Tan Ve fx-1 ax + In{(x+ 1)*(x² – x + 1)"| + The resulting integral of -X+ -1 + C,…

A:

Q: so xe x dx

A:

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…

A:

Q: (9) Evaluate the indefinite integral f X+2 dx x² + 4x 2

A:

Q: 12.)Express lim E(3(x;,)² – 5x, + 2)Ax as a definite integral on the interval [0,1]. i=1

A: The given expression is: limn→∞ ∑i=1n 3xi2-5xi+2∆x    on interval [0, 1]   The definite integral  on…

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. Integrate f over the given interval of x, using…

A: Consider the provided question, fx=sin2x+cos4x, 0≤x≤1. We need to Integrate 'f' over the given…

Q: 2. Find the indefinite integral: S (Vã+ - x + - 1) dx 6 .3 X X

A:

Q: please explain how to do question 7c

A: The given integral is ∫(1-3x)4dx.

Q: Express the limit as a definite integral on the given interval. n *2 lim 2x;* + (x;") Ax, [1, 6] i =…

A:

Q: 60. Is there a value of b that will make Sx + b, x<0 (cos x, x20 continuous at x= 0? Differentiable…

A: A function is continuous at x=c, if LHL at c=f(c)=RHL at climx→c-f(x)=f(c)=limx→c+f(x) A function is…

Q: At the point of discontinuity on(0, 00), the Fourier Sine integral converges to: OA None f(x+) -…

A: Here  At the point of discontinuity on  0,∞ the Fourier sine integral converges to

Q: Consider the integration of f(x) = 1 + e* sin(4x) over the fixed interval [0, 1]. Apply composite…

A:

Q: dx integralini hesaplayınız. x(In x)

A: Fundamental theorem allows us to compute definite integrals using the antiderivatives. It states…

Q: In(x) Differentiate the function F(x) = | cos(e e') dt (for x>0)- 1/x Show and justify your work.…

A: The given function is: Fx=∫1xlnxcosetdt To differentiate the given function.

Q: 2 (F(x) + x³)dx = ? %3D -1

A: Given that the area under f(x) in [-1,2] is 10br2 So,

Q: Set up a definite integral to find the length of the curve  y= (3/4)x(4/3) - (3/8)x(2/3) over the…

A: The given curve is,

Q: 5. Evaluate the integral. (Use C for the constant of integration.) sin³ (y)cos (y)dy

A:

Q: 12. Let a and b be non-negative real numbers. Provide an example of an improper integral of the form…

A:

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: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate…

A: Here, given that h-π4=12, hπ4=1 &amp; ∫-11h(x)dx=2...(1)

Q: 5) Evaluate ehe integral (use c fos Ane constant of integration. tan'cx)cos x) dx

A:

Q: 4. (a) Explain why the integral (1+ x)3 dx is an improper integral. Determine whether the improper…

A: We have to find out

Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

A: Solution of question as follow

Q: Show that integral 0 to infinity  x2 e -x2  dx = 1/2 integral 0 to infinity e -x2  dx

A:

Q: The value of the definite integral fm12 √ex - 9 dx is in the form F(b) – F(a), where a In 9 and b…

A: We have to solve given Questions.

Q: 1. Evaluate the indefinite integral. Hint: U-substitution. 3 dx x In x

A: ∫ 3x lnx dx 3∫ 1lnx·1x dx

Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

A:

Q: 1) Evaluate. Јx cosh ax dx 2) Evaluate the integral. (In x)² dx x3 1

A:

Q: Q7. Using Simpson's Rule evaluate the integral (√x+1) dx using 8 subintervals.

A: In this question,  we have to evaluate the integral ∫08x+1dx using 8 subintervals by Simpson's Rule.

Q: 10. Find the indefinite integral. x – 2 dx x² + 1 -

A:

Q: Determine if this improper integral will diverge or converge dx (x² – 1)4/3 1 Apply this in solving:…

A:

Q: (a) Explain why | dr is divergent. (b) Find all value(s) of t > 0 for which the integral / 1 dx is…

A:

Q: 7. Determine whether the integrals below converge or not. Do not try to evaluate them. (a) 1 dx 1 dx…

A:

Q: Evaluate the definite integral S (1 + 2x) dx using Riemann sum.

A:

Q: lim n→∞  n xi ln(1 + xi2) Δx, [0, 2]   i = 1  2   0     dx

A: