nto Usx) = S K(x5) K($st) f(t) dt d 3 %3D a Us CX) = Sfct)[ [K(x,3)K(3st)d3] dt %3D

Q: 1 dx (1+x2)2

A: Given:

Q: 2. dx find this integral by using Simpson's rule e

A:

Q: 4. Yes, more integrals to solve! 1 dx x/lnx tan x dx COS I b) / e* dx a)

A: 4. It is asked to evaluate the given integral .

Q: 3. (5 marks) Evaluate the integral I = dx. Hint: If you need to evaluate fe da, don't! Try a…

A:

Q: 1 Use the integration formula ax dx = ax + C to find 4* dx and simplify. In(

A:

Q: Q5) Find the integration by using (by part method): S e3X sin X dX

A:

Q: In the integration of (cos y)^2 dy/(1 - sin y), what is the first step to solve the integral?…

A: ∫cosy21-siny dy

Q: S 4x cos(2 – 3x) dx

A:

Q: J, 3x +1 dx 3. Find the exact value of the given definite integral *, 6 dx 4. Evaluate the given…

A:

Q: 5. 5 S x ³e x² dx

A:

Q: -1.30 Find the value of the integral 100 √x dx by using simpson method (n = 6)?

A:

Q: QUESTION 2: Find the approximation for the integral 4 1 S₁ 2x² dx, when applying: the Trapezoidal…

A:

Q: ['Y«) dx (0, Solve the integral equation : = 1+1+?. (x-1)AO, Using L.T and convolution

A:

Q: In the integration of (cos y)^2 dy/(1 - sin y), what is the first step to solve the integral? Select…

A: Given integral.

Q: Evaluate the integral: 3 9x dx

A: Given,          ∫3-9x2dx

Q: Find the value of dx (7x – 2)° If the integral diverges, give "oo" as your answer. -

A:

Q: Evaluate the integrals showing all steps. Give the exact solution. r37/2 sin y dy T/2

A:

Q: 3. Evaluate the integrals: e2x dx x2 е. 3 f. Si tan(2x) dx 3

A:

Q: In the integration of (cos y)^2 dy/(1 - sin y), what is the first step to solve the integral? a.…

A: Consider the integral: ∫cosy21-sinydy

Q: Use integration by parts to prove the reduction formula: п-1 S (In x)"dx = x(ln x)" – n [ (Inx)"-! п

A: 2

Q: In the integration of (cos y)^2 dy/(1- sin y), what is the first step to solve the integral? *

A: Given,          ∫cosy2dy1-siny

Q: What is the particular integral of the equation (D 2+9) y= x Cosx?

A: Use basic properties and formula, get PI of given equation.

Q: Q2:A/ Evaluate the integrals sec (1 + ex) tan (1 + e'/x) dx

A: Integral

Q: !!! 6 cos (x2) Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Triple integral

Q: Q-3: Find the general indefinite integrals of: 1. S cos ntcos(sin(at)) dt 2. SVx +2x dx s dx 3-2x2-4…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: QUESTION 5 dx Compute the integral Jx-2)(x-3)(x+2) by showing all the details of your work. Attach…

A:

Q: cos y S- = dy V1+ sin y

A: Given, ∫cosy1+sin2ydy Now assuming ,   t = siny then dt/dy = cosy dt =cosydy Sustituting the values…

Q: Solve the integral: dy dx. x2 H/4

A: To solve: The integral ∫141∫x2xxydydx. Formula used: ∫xndx=xn+1n+1+C Here, C is constant of…

Q: In(2x + 2) · dx a) Use Trapezoidal rule with n=4 to approximate the integration b) Estimate the…

A: Given function is ∫04ln2x+2·dx   a) fx=ln2x+2 h=b-an=4-04=1 The function values are  x 0 1 2 3 4…

Q: E. Find the indefinite integral. -dv 1+ 7v

A:

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: 2 и…

A:

Q: x² – 25 dx Jx+5

A: Formula: a2-b2= (a+b)(a-b)

Q: 1 dx ? %3D (x-1)3 8-

A:

Q: Suppose you want to evaluate the indefinite integral 2x2020 da using integration by parts. Which…

A: We will apply integration by parts formula by choosing appropriate functions as u and v.

Q: Determine Secos sin 5y dy by using substitution method. Solve each of the following integrals using…

A:

Q: To treat the integral       −36(2x + 1)−2 dx as a constant multiple of one of the form       unu'…

A:

Q: Calculate the integral approximation S6 for 0 -1 4-² dx.

A: In this question we have to find the Integration.

Q: |(16x3 - 3x2 + 4) dx (16х3

A:

Q: Evaluate the integral. 6x2 sin AX dx Step 1 To use the integration-by-parts formula u dy = uvV – v…

A: Given:

Q: Solve the problem. Rewrite the integral 5(1 - z/6) 2(1- y/5 - z/6) dx dy dz in the order dz dy dx.

A:

Q: Evaluate the integrals: (d) ∫(lnx)2dx. (e) ∫tan−1(3x)dx. (f)∫cos4(3x)dx.

A: We can evaluate the first two integrals by using  the integration by parts method. To evaluate…

Q: by taking n = 2 • dx solution of the integral with Simpson's 1/3 method which one?

A:

Q: 5. Evaluate the definite integral (1+lnx)² dx а. 1 dx. b. -1 2x+3

A: Explanation of the answer is as follows

Q: 1 x²y dy dx 2 Jo /0 Jo

A: Consider the expression is, 12∫04∫02x2ydydx Solve the integral as,…

Q: Calculate the integral approximation S6 for 2 2-a" dx. 1 S6

A:

Q: The value of the integral T/2 sin x dx cos(x)e- sin Jo is: Оа. 1-е-1 O a. O b. e- sin 1 O C. С. cos…

A:

Q: S*Sx² sin(xy) dydx

A:

Q: Q.4 Use the integration by parts to evaluate the integral. V3 2 sin-1 x dx

A:

Q: In approximation of 4e* sin(2x) dx by Romberg Integration, R11 = O 2.6842 O 2.9736 O None of these O…

A: Use the following formulae, to estimate the integral ∫abfxdx by the Romberg integration method.…