Suppose that f and h are integrable and that f(x) dx = -1, f(x) dx = 5, h(x) dx = 4. Use the rules in Table 5.6 to find -2f(x) dx [f(x) + h(x)] dx a. b. 7 [2f(x) – 3h(x)] dx d. f(x) dx с. .7 f(x) dx | [h(x) – fx)] dx е. f.

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: 10) Suppose that f is continuous and that f(z) dz = 0 and f(z) dz = 5. Find - 6f(x) dx . -3 -3 A) 30…

A: ∫-33f(z) dz = 0  ,    ∫-35 f(z) dz   = 5find -∫356f(x) dx∫abf(x) dx    = ∫acf(x) dx   +∫cb f(x)…

Q: 10 Suppose that " fx) dx and Ax) dx = -5, and "g(x) dx = -1 and g(x) dx = 3. Compute the given…

A: Given,∫04f(x)dx=7∫02f(x)dx=-5∫04g(x)dx=-1∫02g(x)dx=3

Q: 3. Use the Comparison Test to determine whether the integral cos? x dx is convergent or divergent.…

A:

Q: Evaluate the integral: √ S - (9x²+7x) (x−1)(x+1)² dx = ← +C

A: Given; I=∫-9x2+7xx-1x+12dx   As we know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: 3 Calculate the integral: dx x² V25 + x2

A: Here first put x=1/t and then the expression inside the square root as y^2. As showing in solution

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: dx 7. S x V9x2-1

A:

Q: 1. Evaluate the ff. integral f, (5x6 + 3x³ + 6)dx ·1

A:

Q: 3. Evaluate the following improper integral; -2 2 dx x² – 1

A:

Q: 1. Determine if the following improper integrals converges or diverges dx a. (1+r*)'/3 b. cos(x-1)…

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Q: Evaluate the integral. HINT: 3 x2 dx J2 x - 1

A:

Q: 1) Evaluate each integral by substitution: (In x) dx a)f(x+1)(x +2x)'dx b)fxVx² +9dx 「ズ dx 7x+5 dx…

A:

Q: 12. Suppose that g is integrable and that g(x)dx = -7 and [8(x)dx = 2. d: g(x)dx

A:

Q: 1.1 the integral f cos(lnx) dx . x2 1.2 the integral S x³V1– 2x dx

A: 1.1 Given integral is ∫coslnxx2dx Let u=lnx⇒dudx=1x dx=xdu1x=e-u∫e-ucosudu we will integrate by…

Q: Use Part 1 of the Fundamental Theorem of Calculus (and properties of definite integrals and the…

A: Solve the following

Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: Evaluate the integral. USE TABLE TO EVALUATE dx x/3 + 6x V3- In 3+6x 3+6x+ + C - V3 + 6x - 3 In + C…

A:

Q: Step by step

A: Given integral

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

A:

Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

A:

Q: 3 Evaluate the integral |x V2x +1 dx ?

A: ∫x22x3+1dx We need to integrate the given function.

Q: a) [ Evaluate the integral 4x - 1 (x + 2)(2x - 1) S -dx.

A:

Q: Step by step

A:

Q: #3. Suppose that h(x) is integrable and that ,h(x)dx=1 and S,h(t)dt = 6. Find a. Sh(x)dx b. –…

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Q: the integral S(x³ – 2x – 1)e-*+1dx is equal to:

A:

Q: A b B d a The integral 15x²x³43x - 19 (x + 1)²(x² - 6x +13) can be rewritten as Ax + B D C + ax² +…

A:

Q: 2 Evaluate the improper integral e2a dx, if exists.

A: Evaluate the improper integral  ∫-∞2 e2x dx

Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

A:

Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C…

A:

Q: Consider the following BVP: - 2u 1 1sxs2 dx Using boundary condition u(1)-u(2)-0.

A: Sincei have attempted similar problems, let me solve the given problem step by step....

Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: integral x^2 e^2x

A:

Q: Find the integral. √(x + 1)e 6x² + 12 е 12x dx √(x + 1)e 6x² + 12x dx = [

A:

Q: Evaluate the integral (x – 1)ez xp- x² – 2x + 2

A: The objective is to find ∫-∞∞(x-1)eix(x2-2x+2)dx It is known that, eix is an increasing function.…

Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

A:

Q: Evaluate the integral: x² e3a dx

A: This question is related to Indefinite Integral, we will use Integration by parts formula to solve…

Q: evaluate the given integral.

A: The given integral ∫2x+1xx2+4dx can be evaluated as, ∫2x+1xx2+4dx=∫2x2+4dx+∫1xx2+4dx The integral…

Q: 6. Evaluate the integral dx (4x2 + 1)(x² + 4)

A:

Q: 7. Evaluate the integral. Vx2 – 25 dx х3

A: First we will make a trigonometric substitution of x=5*sec θ then we will solve it and integrate it.…

Q: In Evaluate the integral: Sé e x²+3x-7 x-2 dx

A: Option (b) x22+5x+3ln|x-2|+C

Q: Compute the definite integral 2 dx Vx² + 4

A: First, we need to compute ∫xx2+4dx

Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: 1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

A:

Q: Evaluate the improper integral s dx -2 (2+1)4/3

A: Given: To evaluate ∫-201(x+1)43dx

Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

A:

Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

Q: Evaluate the given integral: x³ – 2Vx dx .3

A:

Q: the integral (dx)/(xsqrt4x2+1)

A: