Suppose d a e R, where a > 0, a ± 1, what is (a*]? dx

Q: Evaluate the following integral. e2 ( In (x?) -dx

A: We can use the substitution method to solve it.

Q: What is the formula that would be used to calculate the trapezoid approximation of ST 2s in x dx…

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Q: Find the following integral: S- -4 /x² dx x3

A: Explained below

Q: 22. How large should n be to guarantee that the Simpson's Rule approximation to e dx is accurate to…

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Q: Find General Solution on this Diffential E Qution by using (uC set) =e +Sin X

A: Given differential equation is y''+y'-2y=ex+sinxfind the general solution

Q: Evaluate the following integral: )dy dx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

Q: 1. Approximate dx using each of the following.

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Q: 43. (In z)² dx

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Q: The value of the double integral 7 1 4xy dy dx is 4

A: ∫46(∫274xydy)dxIntregation wrt y so x will be constant.⇒∫46[4xy22]27dx ⇒∫462x(49-4)⇒∫462x(45)dx

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

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Q: e" cos x dx

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Q: The integral 2n / 14xe dx can be done with the substitution u - and du= dx.

A: Step 3Given,2π∫14xe-x2dx

Q: et Calculate the integral: dx (e – 4)(e* + 5) -

A: Given,            ∫exex-4ex+5dx

Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

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Q: The following improper integral (x² - 1)e***dx

A: ∫0∞(x2-1)e-x+1 dx= e∫0∞(x2-1)e-xdxUsing Integrate by parts:=e-(x2-1)e-x-∫-2xe-xdxUsing Integrate by…

Q: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

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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: Evaluate the given integral. 75 1 dy dx 25 + x 5.

A: We need to evaluate the following interval- ∫05∫x5125+x2dydx

Q: Evaluate 2 dx Using Simpson's 3/8 Rule,taking (h=0.2). Answer:0.80674

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Q: On what interval is the formula d/dx(tanh'x) = 1/(x² – 1) valid?

A: ddxtanh-1x=1x2-1

Q: In(3) e Ver +1 dx In(2)

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Q: Given the integral 4 dx and the substitution information x+ 9

A: Given : ∫4x+9dx

Q: |a² sin(r – 1) dx

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Q: The approximation of x' e¯*dx by Simpson's Rule is O 0.162402 O 0.160603 O 0.160602 O None of these…

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Q: How large should n be to guarantee that the Simpson's Rule approximation to dx is accurate to within…

A: Given:  ∫017ex2dx             where f(x)=7ex2 and a=0 , b=1.

Q: | 17e dx is accurate to within 0.0001? How large should n be to guarantee that the Simpson's Rule…

A: let f(x)=17ex2 differentiating four times to get fiv(x) because the fourth derivative will be non…

Q: 1 dx x(In x)*

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Q: ) 1 1 dx x – 1

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Q: Evaluate the following integral. 9ex dx 1- e 2x

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Q: Find cosh r In(sinh a)dr.

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Q: Evaluate the definite integral. 8. (In x)2 dx Hint: Let u = (In x)2, dv = dx

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Q: How large should n be to guarantee that the Simpson's Rule approximation to 19e is accurate to…

A: We need to find how large should n be.

Q: (e) /a (с) dx e2x 2.х

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Q: Evaluate the following integral arctan x dx

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Q: dy y(ln y- In a+1) dx 1 C = -In 1 C = In O Option 2 Option 1 1 C =-In None of the choices O Option 4

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Q: Solve the folkowing di fferential equotions 1. xdy dx + dy x'

A: Firstly , we can solve for dydx. After that we can see that the equation is an homogeneous…

Q: را Evaluat the following integral by reversing 2 e dx dy

A: It is known that ∫exdx=ex. The order of the integration can be changed by plotting the integration…

Q: Which area in Figure 8 is equal to Suase dx? (4+x²)3/2 (b) 1- 2 u S2 cos u du sin u du (c) y (d) 1 u

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

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Q: The integral dx is Select one: O None. o o o

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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: Evaluate 1- x? dx 0. by Simpson's rale with n=5

A: Here fx=x1-x2 The interval is 0,1 and n=5. Hence the interval is divided into 5 equal parts.…

Q: To evaluate the integral * dx we use the substitution e а. x2 1 O b. 1- x2 O d. x + 1 =t

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

Q: Suppose we wish to evaluate by using integration by parts, where a, bER. Given that we choose what…

A: Let  u=x ; v = e2xAfter differentiating v with respect to x is:dvdx=2e2xdv=2e2xdxAfter…

Q: Given the integral 5x * e7x dx

A: The given integral ∫5xe7xdx can be evaluated by using the integration by parts as, ∫5xe7xdx=∫5xe7xdx…

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: Consider the following integral. 7 - x dx

A: