25. By considering integration round a suitable rectangular contour, show that cosh ar dx cosh nx dx = sec and hence sec cosh x

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral S7 n = 20…

A: we nee to find ∫π4π2ln(tanx)dx,  n=20 a=π4=0.7854,  b=π2=1.5708 ,  y=ln(tanx)…

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

A:

Q: Consider integral x sin(3x) dx  apply integration by parts with formula u=sin(3x) and dv=x dx.…

A: In the question it is asked to calculate the integral of I=∫x.sin(3x)dx using integration by parts.…

Q: Choose among the following suitable to define the given S(e + +) arctan{ dx O By parts, the red part…

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

Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

Q: evaluate using Integration by Parts.

A:

Q: evaluate using Integration by Parts.

A:

Q: Show that ∫0∞ e-x 2 dx = ∫10√(-ln y)  dy  by interpreting theintegrals as areas.

A:

Q: Use integration by parts to show that for n > 2: / sin" x dx: 1 sin- x cos x + /sin-2 x dx.

A: To evaluate: ∫sinnx dx

Q: The value of the integral Vx dx computed using Trapezoidal rule with 2 subintervals is (Rounded upto…

A: The trapezoidal rule uses the area of the trapezoids to approximate an integral. Using the…

Q: How large should we take in order to guarantee that the Trapezoidaland Midpoint Rule approximations…

A: Given

Q: 1. Approximate | sin(x²) dx with 12 subintervals by Trapezoidal rule. 1 Simpson's - rule. (a) (b) 3…

A:

Q: To evaluate the integral |(2x+1)tan Vx dx using Integration by Parts, we should choose

A:

Q: Verify the integration formulas ∫sech x dx = sin-1 (tanh x) + C

A: To verify: The integration formula, Formula used:

Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: What are the new limits of integration after applying the substitution u = 5x + z to the integral s…

A:

Q: Choose among the following suitable to define the given integrations: Sx sin x² dx By parts, the red…

A:

Q: What is the value of the integral ∫2−2 max [1,x2] dx ?

A: This question is related to integration.

Q: 8 Evelluate the double integral: + 3x) dydx

A:

Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

Q: Find the value of the definite integrallo 2 cos ( x ) dx given that the antiderivative for the…

A:

Q: Consider the integral Í dx . For which value of n the error in trapezoidal rule will be less than…

A:

Q: If the change of variables u = x2 - 4 is used to evaluate the definiteintegral, what are the new…

A: ∫24fx dx Here the lower limit is x=2 & upper limit is x=4.

Q: Use geometry to calculate (without integrating): o V16 – x2 dx Note that f (x) = v16 – x² is the top…

A:

Q: Use the 4_segment trapezoidal Rule to numerically integrate. S(0.2 + 25x + 3x²) dx

A:

Q: In evaluating, 2x cos (2x) dx using integration by parts, identify the portion of the integrand to…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 5. Evaluate S (tan(2y) + cot(2y))² dy using integration by algebraic substitution.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | 2 tan (x) sec®(x) dx C must be in…

A:

Q: To evaluate the integral |x sin xcos x dx using integration by parts, the convenient choice is, H=…

A: a. Given integral is ∫ xtan2xdx. Considering u=x and v'=tan2x is the convenient choice for…

Q: What are the new limits of integration if apply the substitution u = 5x + n to the integral sin (5x…

A:

Q: In using the technique of integration by parts, you must carefully choose which expression is u. For…

A:

Q: 1 To find the integral x x cos 7x dx by the parts formula, use u = x and v = sin 7x, as used in the…

A:

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral SIn(tan x)…

A:

Q: 3.) Determine the absolute and relative error that occurs when approximating the integral 32x² dx…

A:

Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: sec? (4x)(3 – tan(4x))³dx

A: Given integral is,  ∫sec24x3-tan4x3dx. Substitute t=3-tan4x.…

Q: Find the indicated midpoint rule approximation to the following integral. .3 2 sin 7x 2 x dx using n…

A: Calculate the delta x and the f(xi) for the given integral.

Q: Use (a) the Trapezoidal Rule integral 1to 4    sin x dx                 with n= 5

A:

Q: What is the value of the integral ∫2−2 max[1,x2]dx ?

A: Value of the given integral is 2x [1- ((x^2) /3) ]

Q: Evaluate the integral. + 2x) cos(x) dx Work must each include tabular method, OR u, v, du, dv for…

A:

Q: I+tgX dx; 2 COS X cos

A: Given: ∫1+tanxcos2xdx

Q: 2. Determine the values of ʼn and h required to approximate fx²sin (-x) dx to within 10% using the…

A:

Q: Evaluate the integral. (x² + 4x) cos(x) dx Work must each include tabular method, OR u, v, du, dv…

A: =∫(x2+4)cos(x)dx Integrate by parts: ∫fg′=fg−∫f′g f =x^2+4, g′ =cos(x)   ↓ steps   ↓ steps f′…

Q: Calculate using integration by parts: x^3 sin(x^2) dx

A: Given: ∫x3sinx2dx

Q: Consider the integral dx . For which value of n the error in trapezoidal rule will be less than…

A:

Q: 5. Use integration to find the exact area outside r = 4 cos 0 and r = 4 sin 0 but inside r = 2.

A:

Q: (a) In(4x) dx

A: Integration by parts:  ∫f(x)g′(x)dx = f(x)g(x) −∫f′(x)g(x)dx

Q: Change the order of integration 2 rIn(r)+1 f(r,y) dy dx Ji Ji

A: