d Suppose a E R, where a > 0, a + 1, what is [a*]? dx

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: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

A: SOLUTION-

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

A: Tpoic- Differentiation

Q: 59. Show that for any number a > 1 -Ina In x dx + e dy = a In a,

A: Given: ∫1alnxdx+∫0lnaeydy=alna

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: 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.

A:

Q: Evaluate I = | x(In z)² dx

A:

Q: N3/4 4 e4x dx 5) 1 + e8x

A:

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

A:

Q: If In = + a?)" dx, show that - (x(x² + a²)" + 21na²In 1]. 2n + 1 1 In

A:

Q: Determine the Equation from the information below: HA: none X-Int: (0, 0) VA: none Y-Int: (0, 0)…

A: The graph of a straight line crosses the x axis at the x-intercept and the y axis at the…

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

A:

Q: e" cos x dx

A:

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

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

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

A: Given,            ∫exex-4ex+5dx

Q: Use Simpson's Rule to approximate the value of the definite integral 2x dx with n = 8. a. 16.9283 b.…

A: Simpson rule formula is: ∫082x4 dx≈∆x3f(x0+4f(x1)+2f(x2)+4f(x3)+...+f(xn))...(1) Here, ∆x=8-08=1,…

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: Q1. Evaluate the following Integral +3 dx

A:

Q: The integral S.¹0 d 10 x²+6 x-8 is improper. dx

A: The given integral is (x2+6)/(x-8) , limit from 6 to 10.

Q: The approximation of - 1 dx by the composite Trapezoidal Rule with n= 2 is x+4 O 0.40833 O 0.40546 O…

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: Evaluate the following integral. 3 5 e dz dx dy -2 4 1

A: Calculation:

Q: Evaluate: dx. x-2 A) In 3 - In(-2). B) The integral diverges. C) In 3 - In 2. D) - In 3 + In 2. In 3…

A:

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

A:

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

A:

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

A: Given : ∫4x+9dx

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: Q1. Evaluate the following Integral +3 dx ,2

A: Given,

Q: A) Evaluate the following integral dx - (x - 1)(x − 2)(x − 3) 10 points

A:

Q: 1 dx x(In x)*

A:

Q: A) Evaluate the following integral dx (x - 1)(x-2)(x − 3) - , 10 points

A:

Q: d In(12 – x²) at æ = 1. dx Evaluate

A:

Q: 2) Evaluate the following integral: (1.3)* dx

A:

Q: Evaluate J by means of Simpson's rule with n = 2m=10 and h = 0.10 = [*exp(-x²) dx Answer in 4…

A: f(x)=exp(-x2)h=b-an=1-010=0.10 table for x and y values x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1…

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

A:

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

A:

Q: S 3* e*dx

A: Integration means addition it is used for adding continuous function which can't be added by simple…

Q: The integral : dx can be evaluated using the substitution u = x – 1. x - 1 True False None of these

A: Recall:   ∫ 1x dx=ln(x)+ c  ∫xn dx= xn+1n+1+c  ; where 'c' is an integrating constant. Substitute…

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: e Tx dx x2 e 3. S

A: We are asked to evaluate the integral.

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: S(a – x)°dx

A: We need to integrate given function.

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: