d Suppose a E R, where a > 0, a ± 1, what is [a*]? ... dx a" In(a) ... A xa*-1 B ... ... xa"-1. In(a) ... D

Q: d In (t2 + 1) dt = dx A) In(x6 + 1) B 3a In (a? + 1) 3x ln (a6 + 1) In (x® + 1) In (e? D -

A:

Q: 5). S 13+1)E dx (Improper Integral)

A:

Q: Estimate the error in using the Trapezoidal Rule with n=8 when approximating the inetegral of…

A:

Q: Find the smallest integer n to guarantee that the error in using Tn to approximate | e dx is e less…

A: The integral is ∫01ex2dx  The error of Tn is obtained by the formula is E=-b-a212n2f''c We want…

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

A:

Q: 17. Find the values of p for which the integral So dx converges. OpE (-1,1) Op21 Op 1 Opsl

A:

Q: Q4 Evaluate the fo ng In10 1- 4sinh? () dx 4 2 cosh(tane)sec20d0 - 4. 0rions in term of

A: (1) To evaluate: ∫0ln 104sinh2x2dx Let I= ∫0ln 104sinh2x2dx We know that 2sinh2x = cosh2x-1

Q: For what value of a, b > 0 is the following integral convergent. dx . x*(1+x*) a + b 1 O a, b>1

A:

Q: 43. (In z)² dx

A:

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

A:

Q: 1) Find the following integals: 14) S(2? -x) dx le) S x* dx la) S x* dx Ic) )치 dr If) Sdx ax ti

A:

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: In (T/e) ( (2- sec?x)eme sec³x sec (зА - х) -dx to be integrable using the formula и" du? ? What…

A:

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

A:

Q: e" cos x dx

A:

Q: +00 dx d.x (1+x)/x

A: Given: To show: The given integral converges.

Q: If f(x, y) = e®¤ . In(16y), then fræ is given by: O 144 e9 In(16y) O - 81 e9 ln(16y) O 81 e9 In(16y)…

A:

Q: 5. Suppose that f(t) is the rate of snowfall t hours after midnight on December 21, measured in r12…

A:

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

A:

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: hoaph fumeten nd be fure at label aut least thne f (u) : Su

A:

Q: Jse the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) 1, dx, 1+x2 I =

A:

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

A:

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: In x d. *dx dx' Find the derivative of the integral as written: O A. Inx O B. 1- In x OC. 1 O D.…

A: Here I am attaching image so that you understand each and every step.

Q: - Evaluate the integral dx using Simpson's th rule e* – 1 3 -

A:

Q: lower bounds Ror o.5 dx dud よx 0.5 Add the se to arrive at am improved estimate of

A: Find upper and lower bounds.

Q: Show dz 4 In= 는I미페 - for a<0. x <

A:

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…

A:

Q: 4. Use the comparison property to calculate if the following integral converge: sin? x dx. | 1+

A:

Q: 1 dx x(In x)*

A:

Q: Apply the open Newton-Cotes formula with 3.5 xe*dx n=1 to approximate 0.5

A: For n =1 , ∆x = b-a3 , and the abscissas are x0 = a+∆x and x1 = a+2∆x . The Lagrange polynomials…

Q: (c) For what values of a <ß is the integral √ √e-at - e-ßt dt To

A:

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: d41 -cosh(x) at x : O is dx41

A: cosh (x)

Q: Choose the letter of the correct answe. 1) x² (xdy + ydx) = (5- xy) dx a) x ln (5-xy) = 1- cx b) -x…

A: We are allow to solve first question only .If you need rest of answer please upload it separately…

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

A:

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 of the following is always true for integrable functions fand g? (x) dx + ) dx ) d - dx ) dx…

A: Option A  is true.

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

A:

Q: Evaluate the following derivative. ar (x In (x10)) a (x In (x'0)) = D dx

A: Given: y=xlnx10 we know that ddxu.v=vdudx+udvdx                                    ..1

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: Let G) = Jtan"(x)dx Find 18G(1) + 140G'(1). %3D O A. 0 O B. 357 OC.No Answer is correct OD. 140%…

A: Given: G(t)=∫t2t3tan-1(x) dx

Q: 7. Evaluate the following integral or state that it diverges: Lo xe* dx

A:

Q: 169 dx Evaluate the integral x( In x)° 13

A:

Q: The function f(z) = sinh(In(z ?)) is equivalet to

A:

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…