Find the value of the improper integral or state that it is divergent. (If it is divergent, enter DIVERGENT.) co 1 dx 11 11 1 lim (t->) 1o 11A 10) - 11

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: Q#01: Find the complete integral of x²p? + y²q? – 4 = 0 using Charpit's method.

A: To find the complete integral of using Charpit's method.

Q: Solve the integral equation S" F(x) cos px dx = ' - P.01 4. .Hence prove that o sin?t -dt = %D

A: Given the integral equation is ∫0∞Fxcospxdx=1-p,0≤p≤10p>1

Q: Evaluate the iterated integral. 8. 15 (x + y²) dx dy

A: When integrating with respect to one variable, consider other variable as constant.

Q: Evaluate the integral: A B C D H|m 1 6 1 |ო 3 √ sin S 1 6 sin(3x)cos(3x) dx

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Q: dæ (xº + 2)² The integral is divergent.

A:

Q: For what value of c does the integral shown below converge? CX 1 1² (²²,- — ) αx dx +7 5x C = 1/5…

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Q: Evaluate the indefinite integral. 2 (t) – 7e' + 8 + 1 + 12 2 sin(t) – 8 cos(t) + sec- dt = +C.

A:

Q: Q.1 A. Compute each of the following integrals. dx. (i)

A: SINCE YOU HAVE ASKED MULTI PAL QUESTIONS IN SINGLE REQUEST , WE WILL BE ANSWERING ONLY THE FIRST…

Q: (d) S tan? 3t dt 5 cos? x - 3 tan x (e) S dx cos x

A: We use substitution method and Trigonometry identities to solve these integration

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

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Q: express L−1[F(s)G(s)] in terms of a convolution integral.

A:

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: Evaluate the improper integral if it exists e'dx: 00 1 -1 0 e.2 O -e 3 O The improper integral…

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

Q: Q1 Find a particular integral. (D² +5D+6) y= e²* (see'x)(1+2 tan x) -2x

A: Given equation,  (D2+5D+6)y = e-2x(sec2x) ( 1+ 2tanx ) Let us solve the equation for y. y…

Q: 2 dx Evaluate the given integral: J, i-6x+10x.

A: NOTE: Refresh your page if you can't see any equations. . for the denominator add and subtract 9

Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: express L−1[F(s)G(s)]in terms of a convolution integral.

A:

Q: Q₁: Evaluat the integral:- 플 S S. sec (cosx) dx dy Sin y

A:

Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2…

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: The improper integral (A) e B) © ⒸO D 1 8 Stoe ex dx is

A: Given that,

Q: Find the integral |(2 + 1)e* dz. (z + 1)e²² dz +C

A: solution is given below integration by parts...

Q: ( a ..    )Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2…

A: Given, ∫01cos2x dx

Q: Which of the following is an improper integral? dx 2 2r+8 B -4 x2-x-2 -1 xe Cos (x)dx -2

A:

Q: Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2   ) dx

A: Given ∫01cos(x2)dx

Q: 1. Evaluate the following integrals. ? cos(r) dt а. Зx2 — 1 dx b.

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Q: can i get step by step help please

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Q: 6. Evaluate any 5 of the following 6 integrals. (a) 12 dx 1 (b) (c) cos(50) de (e) [x²e² dr (d) (f)…

A: To evaluate the following integrals.d ∫xx+1 dxe ∫x2ex dxf ∫arcsin x dx

Q: The substitution t tan- is used to find S- %3D de cos 6 Which of the following gives the correct…

A:

Q: Q1) A-Evaluate the following integrals: 1) S (cos x/ sin? x) dx. 2) S (2x+4)1/3 dx, use x-0 to x=2.…

A: We have to evaluate the given integration.

Q: Evaluate the integral: A B C D 16 1 "Im =|m 1 7/6 دان داww 3 sin(3x)cos(3x) dx

A: We have to find out integral

Q: (a) Evaluate the following integrals: π cos(x) dx dy 4y

A:

Q: Evaluate the integrals: 1- dx TT/2 7cos t sin t dt Jo 2-

A: Given :  Two inetrgal parts with finite limits which we have to solve

Q: 1. Evaluate the given integral Q. /9-y² Q 3r (2x - 2) dz dy dx

A: Note: As you asked solution for only Number (1) so, I answered here only Question (1).

Q: 2. Evaluate the iterated integral. b. So R dx dy -2 2х 4 a. o xy dy dx

A:

Q: 1. Evaluate the given integral Q. √x²+1 (x - y² + 1) dy dx

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Q: Evaluate the integral e'sin e) dx 1- In 2 2 u +3 u + C + C +C cos(e") + C COS -2*+2x + C 21 21

A:

Q: (1+ 1)? dt =D t3

A: Given : ∫1+t2t3dt

Q: Q3/ a) find the integral f 2* * cos2* dx dx b) the integral J e2x+1

A: Explanation of the answer is as follows

Q: Question 12 > x8 dx (29 + 7)? The integral is divergent.

A:

Q: -Jxcar (r<)= o x sin(ñ x) cos (Tx)

A:

Q: Find the forced solution yF (x) at xo Cr³ + c2x³ In(x). 2 to the following ODE in terms of a…

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Q: What is the general solution to the DE, !! dt 2? - 2x + 2? What is the general solution to th O In…

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Q: Evaluate the integral. S"S"S" sin@u + 2) du dv dw A) n cos 2 B T cos 2 C)를 T2 cos 2 D T2 cos 2 /3

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Q.1) Evaluate the following integral ez dx (2e2 – 4e* – 1) - -

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Q: 1. Evaluate the given integral Q. Q - CC² LL- (x - y) dx dy y²

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Q: Solve for F(x) the integral equation F(x) sin xt dt = {2, 1<t<2. [0, t22

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Q: (a) Use integration by parts to evaluate T/4 | 0 sin(20) dð . (b) Use the substitution u = 1+ x to…

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Q: Find the integral of t/(t^4+2) dt

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Q: Find the exact value of the integral. Question 1 4 V2 + x'dx dy

A:

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.