4 y 2 4 10 12 -2- -4 -6 2 (a) dx Number 4 (b) f (x) dæ Number (c) f (x) da Number %3D -co

Q: Find the Particular Integral for the given differential equatiorn d²y dy +3- dx +6y =2x²+x+5 dx2…

A: using expansion,         (1+x)-1 =1-x+x2 -x3+...

Q: 1. Evaluate definite integral. [(2 - y)-y]dy 0.

A: Consider the given integral: ∫042-y-y2dy

Q: 7. Evaluate the following integrals: a. S cosh x sinh x dx b. dx S- 2 + 2x + 3 C.

A:

Q: `s): The area of the surface obtained by rotating the curve y = ln(3x - 2), for 3 ≤ x ≤ e², about…

A:

Q: In the given equation/s as follows , use substitution and partial fractions to find the indefinite…

A: We know that, ddx(cosx)=-sinx We substitute cosx=u in the given integral and then proceed to…

Q: 4. Evaluate the given integral. |(x + 1)(x – 3)| dx -2

A: Solution:Given∫-20(x+1)(x-3)dx =∫-20(x2-2x-3)dx= ∫-20(x2-2x-3)dx= x33-2x22-3x0-2=0--83-4+6=23

Q: 5 Find the following indefinite integrals. 10 a. f(x+2)' dx b. J d. [4 (3-&x) dx c. (3x-7) xp-

A: c)

Q: 2. Compute the following. When evaluating the definite integral, change the limits of integration.…

A: (a).  The given integral is: ∫x21+x35dx

Q: 14. Evaluate the integral. 4 (y - 2)(2y + 1) dy

A: Given that : The integral is ∫04 ( y - 2) ( 2y +1) dy

Q: Q1: A. Find of four of the following: dx 1. y = x sin-1 x +v1– x² 2. y = (x2 + 2x) tanh(x + 1) 3. y…

A: See the details solution in below

Q: 1. Find the definite integrals of the following functions : (a) L. 4.x dx (h) dx ex +1 -2 0. (b) /…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: If you are asked to find the indefinite integral of f(x) = x ln(x), and you are told to integrate by…

A:

Q: 7. Determine the following antiderivatives. cos (x), dx b. dx sin(x) a. sin(x)cos(x) dx d с. tan )dx…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: Q2/ Find the value of the following integrals: 1- |((x+y)dx + (y – x)dy), when cis given by, x = cos…

A: The integrals in the form ∫C(x+y)dx+(y-x)dy involve the integration over a particular curve C. In…

Q: 10. Evaluate the definite integrals by u-substitution. In5 Te(3-4e) de ( 2 cos 3x dx b. а.

A: a. ∫0π62 cos3x dxb. ∫0ln 5ex3-4ex dx

Q: ∫(−6x6−2x3−4)dx

A:

Q: Q2/ Find the value of the following integrals: 1- |((x+ y)dx +(y-x)dy), when c is given by, x = cos…

A: We have to evaluate the integral is ∫cx+ydx+y−xdy. where c is given by x=cosθ, y=sinθ and 0≤θ≤2π.…

Q: 5. Evaluate the following integrals: sin x (1) f dx (ii) [Vsinx cos xdx (iii) -x' dx x* +3x? +2 V1+…

A: Dear student,                      According to our guidelines we are supposed to answer only first…

Q: 2. Evaluate the following integrals. 6 a) dx x² – 3x b) | 4.2? cos(x³ + 2) dæ 4x2 c) / 4x² ln x dx

A:

Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

A:

Q: How do I find K of the integral e^(x^2/2)dx on the bounds from 0-2 what is E_T? and what must n…

A: Given: The error in trapezoidal rule is given as:

Q: Find the following indefinite integrals subject to the initial conditions a) y'= with y(1)=0 x²+6'

A: topic - differential equations

Q: 1. Sketch the graph of the function y = f(x) = 3 – V4 – x² over [-2, 2] and use this to evaluate the…

A: Given: The function y=f(x)=3-4-x2,             Interval: [-2,2]             Integral:…

Q: 2e Consider the indefinite integral dx: (e2z + 3)* This can be transformed into a basic integral by…

A: Given,

Q: If the change of variables u = x + 1 is used to evaluate the definite integral f(x) dx, what are the…

A:

Q: 1.) Find the equation of the line tangent to f(x) = 6 ln(7– 3x)+5e-4 – 6x – 2 at x = 2 2.) Find the…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: 5. Evaluate the following improper integrals (if not shoW Wny). x² dx a- 00 4 1 dx -2 x+2 b-

A: To evaluate the improper integrals.

Q: 1. Find the following integrals using the graph below: g(x) dx 24 g(x) 4 g(x) dx )dx g(x)dx

A:

Q: 5 Find the following indefinite integrals. 10 b. J- S(x+2)' dx a. (3x-7) xp-

A:

Q: If the definite integral of (1 + sin y)dy with lower limit equal to zero is π+2, its upper limit is…

A:

Q: Find the value of the following definite integrals. Show your solution. 1. f(x¹+4) dx 2. (cos x +…

A:

Q: 2. Evaluate the following: 1 - dt 1+t? d ctanx а. dx 2 b. f(8-2x) dx x' +1 dx x+1 С. 3. Evaluate the…

A:

Q: 7. Evaluate the following integrals. 5 a) e dr -5 .2 b) (y – 1)(2y + 1) dy

A:

Q: 11 By reversing evaluate the -3 -9 ffix the orders of integration following integral x cos(y) dy dx

A: Given integral ∫03∫x29 xcosy2dydx The region bounded by  y=x2 , y=9 , x=3 and x=0

Q: dz

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

Q: 2) Evaluate the following integral: L(a - x- 4x³ + 2x*) dx (a) analytically (b) single application…

A: Given Integral: ∫-24(1-x-4x3+2x5)dx

Q: 1. Use properties of the definite integral to solve the following problem. f (x)dx = -3 and f(x)dx =…

A:

Q: 7 So Suppose f(x)dx = 6, f(x)dx =5, and g(x)dx = 8. Evaluate the following integrals. 2 2

A:

Q: 9. Calculate the following definite integrals by hand. (a) x² + 4x dx (b) cos(x) dx (c) o JE 3 dx

A:

Q: Q4 The area between the curves y = -3 cos (z) – 3 and y = 3 cos (2) – 6 on the interval (0, 7) is:…

A:

Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(x) = 1 In r 2 - 4* where…

A:

Q: 1/2 2. Evaluate ( x*(1– 2x)°dx

A: Given: ∫012x41-2x3dx

Q: 1. Determine the following indefinite integrals: S (Ax-1 - Bx-3 + Vx") dx a) ez (wt) – cos(Ewt) )…

A: A=2.6, B=6.4, C=2.6, D=3.4, E=2.7 To find:-

Q: 1. Evaluate the following integrals x² + 6x -dx (a) | x³ cot2(x4) cosec² (x*) dx, (b)|Tr3 – 10 – 5x²…

A:

Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

A:

Q: 16 Suppose we know that " (35(x) – 2) dr = 6 and that :[ #f(x²) dx = 8. Use this information and…

A: We have, ∫4163fx-2dx = 6 ∫04xfx2dx = 8 To evaluate: The value of ∫04fxdx

Q: 17. Evaluate the following integrals. 4 2 a) S - 2* + csc² x dx 2x. - 5 1–x² -4 b) Llx| sin x dx

A:

Q: /4 1.* Use the following property of the definite integral to estimate the definite integral:JCcos x…

A:

Q: 9. Which of the following integrals can NOT be computed using the methods we have covered so far? a)…

A: We have to choose the integral which is not compute by simple integration method

Q: Q2/ Find the value of the following integrals: 1- [(* |(x+ y)dx + (y - x)dy), when c is given by, x…

A: The line integral ∫CF1dx+F2dy involves the integration over a specific path. In this problem, we…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.