D 3 (x+z) dx 2) sin Con) de 3 3dx 2

Q: Solve the integral equation | F(u) F(t – u) du = 16 sin 4t.

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Q: 3 Which of the following is equal to sec 2 x tan?x dx to obtain the correct indefinite integral? A)…

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Q: S 6x®cos (x³) dx „8, ,3•

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Q: (b) 'elz)x d: 1

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

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Q: 4) l a sin(ex) cos g dx 3 dx 5) (x - 2)° 3

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Q: 8 cos" 2πt dt

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Q: Solve the integral: A B с 1 √√x+x √√ Sin/1+x²|+c -In +C 6in|5+ x²|+C с {in/1+x³ |+c C dx

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Q: 3. 4.x sin(4x + 5) dx

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Q: Evaluate the integral. *1/2 7 cos-1(x) dx Jo

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Q: x² + 2 xp (х — 2)(x2 — 2х + 2)

A: The given integral is: I=∫x2+2x-2x2-2x+2dx   We know that; ∫1ax+bdx=1alnax+b+C

Q: QUESTION 2: Find the approximation for the integral 4 1 S₁ 2x² dx, when applying: the Trapezoidal…

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Q: To evaluate x² /1-x² dx using trigonometric substitution, what is the new integral in terms of 0 ? A…

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Q: Solve the following indefinite integral. Show complete solutions. 1. S (9z² + 14z – 2) dz -

A: ∫(9z2+14z-2)dz

Q: s (e² + 4 cos 8z dz 1+sin 8z,

A: A detailed solution is given below

Q: Evaluate the integral. 1/20 cos,10x sin 10x dy dx

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Q: Solve the equation by Cauchy's integral formula. ez dz z - 5

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Q: Evaluate 1. 2. the integrals: (1-cos²x) 3/² dx Se* sec³ e* dx

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Q: Use substitution to evaluate the indefinite integral | cos³t sint dt. [Hide Solution] cosʻt + C 4

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Q: Evaluate the integral. ,3π/2 20) 6 cos 2x dx T/2

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Q: Evaluate the following integral. 2 5 e 2,2 dz dx dy -221

A: Given: ∫-25∫25∫1ex2y2zdz dx dy ⇒∫1ex2y2zdz=x2y2∫1e1zdz       ...constant out⇒x2y2lnz1e…

Q: cos y S- = dy V1+ sin y

A: Given, ∫cosy1+sin2ydy Now assuming ,   t = siny then dt/dy = cosy dt =cosydy Sustituting the values…

Q: This question requires a full written solution. Find the integral 5x2 - 3x +2 dx (r + 1)(r2 +1) I =

A: Integration by partial fraction

Q: sin-cos-sino de has the form 2 -F(e) +C. What should be the value of e to make F(e): The resulting…

A: We will find the value of theta.

Q: (4) / | Va In x da (d) In x dx x2 (e)

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Q: In evaluating / *sin³(2x)cos(2x) dr by substitution, if u = sin(2x) then what will be the resulting…

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Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

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Q: 2x-3 dx J9x2-12x+4

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Q: Work out the value of the definite integral (5x +2)°dx 1 [B – CP], where A, B, C,p are positive…

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Q: 7. Find the indefinite integral. (a) / 3 cos(") dz /32c0 31 dr

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Q: The resulting integral of sin-cos-sino de 2 2 has the form -(0)+ C· What should be the value of o to…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Evaluate the integral. cos(0) d0 π/2

A: Definite integration

Q: sin t ( 10 + COs t)3 7 - sin 4x dx |

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Q: Evaluate the iterated integral. ra/2 7 cos (x + y + z) dz dx dy

A: To find the integral.

Q: Evaluate the integrals ∫(2θ + 1 + 2 cos (2θ + 1)) dθ

A: To evaluate ∫2θ+1+2cos2θ+1dθ

Q: Given the integral of S cos² x dx,

A: O integrate the given function.

Q: du 2. f 1-cos? 2u

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Q: -cos-sino de has the form sin 2 2 -F(0) +C. What should The resulting integral of 4 be the value of…

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Q: In evaluating | *sin3(2x) cos(2x) dx by substitution, if U = sin( 2x ) then what will be the…

A: First we put sin(2x)=u and then differentiate both sides with respect to x and solve it. 2cos…

Q: Evaluate the iterated integral. cos(e) 7r° sin(0) dr de /3

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Q: In evaluating sin³( 2x)cos(2x) dr by substitution, if 4 =sin(2x) then what will be the resulting…

A: By the given substitution we can solve it.

Q: Solve A = sin(t²) + t, x(0) = 20. It is OK to leave your answer as a definite integral. %3D %3D

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Q: 1 x²y dy dx 2 Jo /0 Jo

A: Consider the expression is, 12∫04∫02x2ydydx Solve the integral as,…

Q: Evaluate the integral: 30dx / (1-cos(5x)) The solution to the integral is -6(Cot(5x) + Csc(5x)) + C…

A: Multiply by (1+cos(5x)) in numerator and denominator.

Q: Evaluate the integral.

A: Given:           ∫0π2cos3x sin 2x dx Rewrite using trigonometric identity: sin 2x = 2 sin x cos x…

Q: To finish up, make sure you understand the basic integration commands in Mathematica by using it to…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…