1. Use a substitution to find (6x2 2)e*+¤ dx showing working.

Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

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

Q: 20. Use u substitution to evaluate. S secrtant 1+secx dx

A: Evaluation of the indefinite integral by substitution method

Q: 2- Find O for: y= In (x+5x) dx

A: Tpoic- Differentiation

Q: 1. Evaluate (i) dy dx, 3

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Q: Evaluate S 2y²sinxy dy dx

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Q: 2. determine ∫12/5-2x dx by using substitution technique.

A: ∫125-2xdx  This is the integral given to us.we need to perform valid substitutions to evaluate the…

Q: 25-x2 In dx , if we letu=V25-x² , then udu= – xdx.

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Q: (a) By using the substitution, u = 1 + x*, or otherwise, find x3 -dx 1+ x4

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate I = In(2 +3/x) -dx, 12…

A: To use the composite Sympsopns 1/3 rule with step length h=0.4.

Q: 57. Verify that S2 yields the exact value of | (x – x³) dx.

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Q: 73. Use the definition of |x\, the chain rule, and the fact that (In x) = - for x > 0 to prove that…

A: Given, dlnxdx=1x, x>0 from definition of x x=x ,     x>0 -x ,  x<0  if x>0 then d…

Q: Obtain a-(In x)? dx.

A: Given,  ∫x-5(lnx)2dx

Q: (3) SaʼIn a dx =

A:

Q: 4. Find an approximate value for fo In 1+x³| dx.

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

Q: d Prove In Jax| dx In x for any constant a. dx

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Q: 4 5y²-8X+6) dx =?

A: To evaluate the given definite integral

Q: Drove that 3 e dx converges to 9 3e

A: Explanation and solutions is given below.....

Q: Derive a formula for In x dx where a. nt-1 b. n=-1

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Q: 5 2 +2 ) dx using Estimate I - n = 4 subintervals and (a) Left endpoints. (b) Right endnoints.

A: solution:-I=∫152x+2dx,     n=4f(x)=2x+2∆x=5-14=1(a) Left end pointI=∆xf(1)+f(2)+f(3)+f(4)…

Q: find x for which = 0. dx

A:

Q: 5. /2хе-2х dx

A: Given:       ∫ 2xe-2xdx

Q: (a) Consider the task of approximating e-4=* dx using the Composite Trapezoidal rule. How large…

A: As per bartleby guidelines we only give first question answers.

Q: Evaluale the to 312 bwiny dx 12

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Q: IN SA Coefticients 4 Linear in two vanabtes: (x-34+4) dx+2(x-ソ-2)dy

A: In the question it is asked to solve the equation using coefficients linear in two variables:

Q: 2sinh cosh -dx 3cosh? * 2

A:

Q: d Verify coth x = - csch² x. dx

A: Differentiation is the rate of change of some variable with respect to the other variable. If a…

Q: Show that esin(x²)dx < e– 1.

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Q: In 8) * dx Integrate and evaluate the following

A: we have to integrate the following

Q: Use the Chain Rule to find dy/dx of the following. 1. у3 (4x3 -Зх? -х -5 )

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Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

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Q: x² dx 4

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Q: In 3 by Pots tien 3) S (4 - x)e"'dx calculate without integre (f Ju

A: Given,

Q: sec2 X dx 3

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Q: 4х-6 -dx х2-8х+20

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Q: Compute dx using the techniques as presented in class and in our textbook. Show all 2x +5x-3 the…

A: we first factor the denominator

Q: et dx 5-e

A: Given integral is

Q: can this be evalnated by using L'HUSpital's Rule? im x2 3x+ 2 sin(x x)

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Q: 18 2 6x dx using n = 2, 4, and 8 subintervals 2

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Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: 1. Evaluate the integral 2 dx x2 +4x + 20

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Q: 6. Evaluate the integral. x³e2x dx

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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: 1. Find b such that |(a) In 3. dx is equal to х (Б) 3.

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+37) -dx, 1+x?

A: According to the fundamental theorem of calculus ∫x0xnf(x)dx=F(xn)-F(x0), where dFdx=f(x). The…

Q: In x25+x dx , we let x= 5sine.

A: ∫  x225+x2dx

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

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Q: Without using a calculator, determine d/dx{2e^3x *cosh 4x−e^7x} in simplest terms.

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Q: Q/ Find an integating factor for the diff- equ. 2y dx + (3y-2x)dy20? to

A: Conversion of non exact differential equation  to Exact differential equation. Given differential…

Q: 12) a) Use either the Trapezoid OR Midpoint Rule to estimate [ In(1+e* ) dx using at least four…

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