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

Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 1 = [ exp(-x²)dx Note that this…

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Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

Q: Evaluate the integral: integral fom 0 to pi/2 sin^2 x cos^2 xdx

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Q: Use the Table of Integrals to evaluate the integral. T4 - 9 sin e sin 20 de 4 – 9 sin 0 |

A: We use substitution to integrate the given function.

Q: Consider the integral 7x dæ 1+ x? 00 If the integral is divergent, type an upper-case "D".…

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Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 J = exp(-x²)dx 0 Note that this…

A: The trapezoidal rule uses the formula:∫abydx=h2(y0+2(y1+y2+y3+...+yn-1)+yn)  to approximate the…

Q: Evaluate by algebra dx 1. S 3 1+ √x+1

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Q: Evaluate the integral. In 2 2 e sinh 0 d0 - In 10

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Q: Evaluate the indefinite integral. asin (a)cos(2)dz: + C %3D

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Q: Evaluate the following integrals: (a) /sin°(2) dr tan (3r) dr (e) in

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Q: a) Evaluate the integrals using appropriate substitutions. dx Sino i)S i) f de Cos? 8+1 1+16x2

A: as per our guidelines I am solving only first question with both parts a(i) ∫dx1+16x2ii ∫sinθcos2θdθ

Q: [sin(In x)+cos(In x)]¯ dx

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Q: Evaluate the definite integral (from 5 to 7)∫(d/dt (2+2t^4)^(1/2) dt using the Fundamental Theorem…

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Q: Find the answer to this integral:

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Q: I know it’s u-sub, but I forgot how...

A: Given information:The given integral is

Q: 52. Use the substitution u = tan x to evaluate the integral dx 1+ sin? x

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Q: 39. Use the definition of the integral to find the exact answer to x*dx , that is find lim f(x, )Ax.

A: We are asked to evaluate the integral using definition of integral

Q: Use ff(x) dx = F(b) – F(a) to evaluate these integrals: 4 x²e** dx 2. sin x dx 2 In x dx (

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Q: evaluate the integral fromn 0 to pi/2 (cosx)^3

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Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫(x + 1)12…

A: Given: ∫12x+1dx for evaluating this integral we substitute u=x+1 now differentiate both side with…

Q: what is the integral of e^(-2a|t|) from 0 to w

A: Given integral: ∫0we-2atdt

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫ cos (2x +…

A: ∫cos2x+5 dx Now put 2x+5=u Differentiating with respect to x, we get 21+0=dudx⇒2 dx=du⇒dx=du2

Q: The resulting integral of sin -cos-sino de has the form -F(0)+C- What should be the value of e to…

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Q: b) Evaluate the integrals using Part 1 of the Fundamental Theorem of Calculus. 2. L, 4x(1 – x²)dx…

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Q: Guess the value of  integral 0 to infinity    x n e -x dx  , when is an arbitrarypositive integer.

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Q: The indefinite integral Vx +1 dx may be solved by substituting u = x² +1 to get | vūdu. O True O…

A: ∫x2+1dxPut x2+1=udifferentiate w.r.t.x2xdx=dudx=du2xdx=du2u-1I=∫udu2u-1 Therefore it is false that…

Q: Which of the following improper integrals are finite and well- defined? (Tick all that apply) /2 O…

A: some improper integrals are given, we have to find finite and well defined

Q: Evaluate the definite integral. 5x /2 2ecos ( z) sin(z)dz

A: We need to evaluate the following integral I = ∫05π22ecosxsinxdx…

Q: Evaluate the integral, if it exists.  ∫01Sin (3 π t) dt

A: Given the integral ∫01Sin (3 π t) dt We need to evaluate the above integral.

Q: Define the following improper integrals integral -1 to 0  f(x) dx

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Q: Sy² sin(3y³ + 4) dy

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Q: The integral of sin2 3xdx is x 1 -x +A + C, What is the value of A if x =-. 4 O -1/12 O 1/12 O 1/18…

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Q: Evaluate the following integral using the Trapezoidal rule with n = 10 and h = 0.2 In (x² + 1)e co**…

A: According to the trapezoidal rule, the definite integral of a function fx over the interval a,b can…

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: To evaluate the integral using Fundamental Theorem of Calculus I=∫1311+x2dx

Q: use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

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Q: 1. Set up the following improper integrals by definition. sin(x) xe-x³ dx dx 2? — Зх — 4 а. с. 7 et…

A: Solution b: Given integration is ∫17exx-1dx Here 1 is the only point of infinite discontinuity So we…

Q: Evaluate the following integral using the Fundamental Theorem. x-1 dx

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Reduce the following integrals to polynomial type integrals, using an 1) appropriate and explicit…

A: Topic = Integration

Q: In evaluating /x V4- x dx by substitution, if 4 = 4 – x then what will be the resulting indefinite…

A: ∫x4-x3dxu=4-x→dudx=-1→du=-dx

Q: Evaluate the integral 10 cos(In(x)) dx, x > 0

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Q: 2.S x² -4 X -dx

A: Note: Asper company guidelines, we are supposed to answer the first question only. Kindly ask the…

Q: Evaluate the integrals ∫cos t/1 - sin t dt

A: Given :           ∫cos t1-sin tdt

Q: Evaluate the integral of sin 6 (x) dx from 0 to Tt/2. * 5п/32 2n/17 T/32 3Tt/32

A: Given: The objective is to integrate the function sin6(x)dx from 0 to π2.

Q: TU 2. fz sin² x cos4 x dx J

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Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: Given, ∫0π42cos(x)dx

Q: Define the following improper integrals integral -1 to  1 f(x) dx

A: Given integral is,

Q: Use the special or Bessel function to solve TWO from the following integrals In x 1. [ dx x* +1 2.…

A: It is given that

Q: e) S 7 + 2sec(2x)tan(2x))dx 1+x

A: To find: ∫71+x2+2sec2xtan2xdx

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: Evaluate the following integrals using theFundamental Theorem of Calculus.