Evaluate 19191 x2 dx 1)3 3 Estimate the integral with n = 8, use (A) Trapezoidal Rule (B) Simpson's Rule dx Vx2 + 16 Evaluate Sin (x) Cos (x ) dx

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: Evaluate the iterated integral. 5 sin(x + 6y) dy dx

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Q: 14e" dx 1+ e20

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Q: tan (In 4x) cos (In |(2x)"|)|+C. what is b? The integral of dx is b In A B 2 4 4

A: Given :  ∫tan(ln|4x2|)xdx=bln(|cos(ln|(2x)a|)| +C   To find : Value of b

Q: 11. Evaluate the following integrals. sinx dx 1- cosx dt fxsec' x dr b) a) c) t2 +81

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Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: 2. Use a substitution to change the integral into one found in the table of integrals, then…

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Q: Evaluate the iterated integral: 2 sin(xy) dy dx п/2 1

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Q: The value of the improper integral 42 x² e¯¤* dx 1 - 14e 14e-1 - O 14e-1 O 42e-1 O – 42e-1

A: Explanation of the solution is given below...

Q: π 7. fz sin¹x cos¹ x dx

A: To evaluate the following integral by using Walli's formula.∫0π2 sin4 x cos4 x dx

Q: b) Evaluate the integral In 5 (x + 1)²e* dx

A: Given integral is ∫0ln5x+12exdx

Q: 1. Find the integral of f xe¯*dx using Trapezoidal with Romberg with k = 3.

A:

Q: 2. Use the Simpson's rule to approximate the definite integral and determine the corresponding error…

A: The Simspon's rule is used to calculate the numerical integration of the function. The formula for…

Q: Use Simpson's rule to find the value of the following integral e-3x dx where n=4 0.1

A: By the Simpson's rule, ∫abfxdx≈∆x3fx0+4fx1+2fx2+4fx3+...+4fxn-1 here n is 4, a = 0.1 and b=0.9. Then…

Q: 2. Compute the following integrals. tan"(2) sec"(r) dr. (b) sin*(x) tan(x) dx.

A: (a) given that a integration of tan3(x) *sec6(x) Here we compute this integration. We know that tanx…

Q: Evaluate the integral of sin^6 x dx from 0 to T/2.

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Q: Evaluate the integral 11-x²4-x²-y !!! 0 3 x dz dy.dx.

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Q: TU 8. fz sin¹x cos5 x dx 2 0

A: To find the value of the given definite integral:∫0π2sin4x cos5x dxWalli's Formula:∫0π2 cosnx dx=…

Q: a) Evaluate the following integrals 1) xe3*dx 2) | x2 sin x dx 3) | x sin 2x dx

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Q: 5. Evaluate the integral: Jsin?x cos'x dx

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Q: Q2:A/ Evaluate the integrals sec (1 + ex) tan (1 + e'/x) dx

A: Integral

Q: Evaluate the integrals: A: So So x sin y dy dx

A: ∫0π∫0xx siny dy dx

Q: II. Evaluate the following integrals: 7 ax 52X+7 13. [ sin x 2 - cosX (1x dx 14. S MA sec² 3x -dx 1…

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Q: Calculate the iterated integral x² ,3 sin x dy dx.

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Q: a) Evaluate the following integrals 1)/ xe dx 2) x2 sin x dx 3) x sin 2x dx

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Q: 3. a. b. Evaluate the following integrals 2dx dx cos²x√4 tanx - tan² x sin(√x)dx J I sin

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Q: y= cos 3x, for 0sxsn a. Which of the following is a simplified form of the integral? 元 OA. -3 cos 3x…

A: Formula Used: length of arc:

Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

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Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

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Q: Q3. Find integral of ( by using Rectangular rule): -38 L Sin(x) In(x + 2) dx , n = 7 24

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Q: 2. Find the integral of xe*dx using Simpson's 1/3 Rule with n = 4.

A: Simpson's 1/3 rule for integration :-  here 'h' is difference between each interval which are…

Q: Evaluate the integral. (Use C for the constant of integration.) COS s-1(x) dx

A: Let arccos(x)=t x=cos(t) dx=-sin(t)dt So the integral becomes - int t sin(t)dt =-t int sin(t)dt+int…

Q: 11:32 E O 1 Evaluating the integral f In(x)dx, where x> 0 yields:

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: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

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Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: Evaluate the integral. S(e* +8e -*) dx | (e 4x +8 e -x) dx =[(Use C as the arbitrary constant.)

A: Consider the given integral.

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: Evaluate the integral. • T/3 L 3 sin° ( 3x ) dx Зx) dx

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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: Set up an integral that represents the arc length of the function g(x)=sinxg(x)=sin⁡x for the…

A: We need to set up an integral that represents the arc length of the function g(x)=sinx for the…

Q: 2. Using an appropriate method, compute the following integrals. dx x² + 3x + 2 (i) sin³x cos*x dx…

A: (i)

Q: 57 Evaluate the integral |[xy dy dx. 12

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Q: 3+n (2x) dx By specifying the +ype of examine it by explainings conveyere integral, x --

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Q: 9/u The evaluation of the Integral of S° sin2x cos4x dx is

A: we have to integrate

Q: 1. Evaluate the trigonometric integral. (1) [20sin² (2x)cos (2x)dx (ii) S4ta dt

A: Given integral is: I=∫20sin22xcos22xdx To solve this integral we will use the following…

Q: In(x) -dx Evaluate the integral m(2)

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Q: Q5. Approximate the integral Sin(2x)dx (i) Using composite Sympson's rule with n = 2,4 and

A: As per the policy of bartleby the provisions is to solve only one question at a time so I am solving…

Q: A. B. Evaluate the following integrals using substitution method: (³-1) ²/3 √2 5.² 0 √r sin (1 + x²)…

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Q: Find a particular integral for d^2y/dx^2+dy/dx= sin x

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