3. Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal rule. 5 3 cos y dydx 4 2

Q: The particular integral for (D2 + 12)y = cos20z is O yp (cos20z) 388 (cos20z) O Up 412 Yp = (cos20z)…

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Q: 6.Solve the following boundary value probletn: at2 U(0, t) ='U(x, t) == 0 U(x,0} = sin x + 2sin 2x…

A: To Solve: The boundary Value Problem : ∂2U∂x2 = ∂2U∂t2U(0,t) = 0U(π,t)=0U(x,0)= sin x+2 sin…

Q: 7. Evaluate the integral (16 – 2? – y?) dV where E is the solid hemisphere x² + y² + z² 0

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Q: 3 dz Calculate th integral o 2-2 (2=4)and (2=5) a)0,6Ti b) 6 i, 6 Ti c)0,2Ti

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Q: 1 To evaluate the integral J dx, we substitute x = 3 tan 0-4. (z²+8z+25)*/2 Select one: O a. True O…

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Q: Find the complete, singular and general integrals of p3 + q3 = 27z. %3D

A: We have to find the complete, singular, and general integrals of:  p3+q3=27z

Q: Evaluate the integral. cos y dy sin 2y + 2 sin y – 3

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Q: T 3. fz sin4 y cos7 y dy 2

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Q: 1. Evaluate the following multiple integrals: 2 252 cos y dædy

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Q: 7. Express the solution of y" + 2y' + 2y = sin (3t) convolution integral (you don't need to evaluate…

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Q: 9. I'Ve* – 1 dx, n= 10

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Q: 2 c2 Reverse order and evaluate the integral S, 2y2 sin(xy) dydx

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Q: 1) Evaluate the following iterated integral. 2/2 sin(2y) SS dydx y 0x

A: Use change of order of integration.

Q: I.Evaluate the ff. iterated integrals. • 7d/2 ptan y sec y 1. .3 cos' ydxdy JJ

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

Q: 19. fy/6 + 4y – 4y² dy

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Q: I.Evaluate the ff. iterated integrals. еЗл /2 сл /2 2. cosysin2x dy dx

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Q: Find the product of the integral In(3) S Som) xy e*y* dxdy

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Q: (a) Calculate the iterated integral 3 7/2 SS(v+y° cos x)dx dy -3 0

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Q: 4. Use the substitution formula and evaluate the following integral: dy -1 y/4y² – 1

A: This question is based on the substitution, make a substitution for y such that the denominator part…

Q: 4. Solve the triple integral below using spherical coordinates IIT √√√x² + y² +2²dzdydx

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Q: 5-Evaluate the following integrals du a) Vu (1+u) a/2 5/2 1 1 b) S cos 0 d 0 sin' 0 sin? 0

A: We will use the Substitution Method to solve both parts (a) and (b) of given Integral.

Q: Estimate the value of the integral 4- x²y2 dA, S = {(x,y)| x² + y? 0} |

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Q: Evaluate the integral 35 dz 4 by making the substitution u = x* – 6. +C

A: integration

Q: 1. Evaluate ∫(6w+12) sin^2 (w/9) dw by using integration by parts technique.

A: givenI=∫(6w+12)sin2(w9)dwwe know trigonometric…

Q: 1 Suppose we perform the substitution u=3+vx in the integral dx . (3+vx)4 What is the resulting…

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Q: Evaluate the iterated integral. 4 5 6 (x² + y² + z²) dx dy dz -4 0 0 5 6 (x + y? + 2? )dx dy dz = i…

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Q: The particular integral of (D2 + 1)y = cosx is -zcosz 2 -zsinz 2 ICOSI zsinz 2 O None of the choices

A: Find particular integral (P .I)

Q: Solve the double integral J, J, (1+ xy)² dydx In n(금) O 2ln(5) – In(3) O In(3) – 4ln(5)

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Q: Given: J5x2 cos(3x³) dx. If U=3x°, then the resulting integral is Jf(u) du. Find 4

A: I=∫ 5x2 cos(3x3) dxu=3x3du = 9 x2 dxx2 dx =du9which gives;I =∫ 5 cos(u) du9I =∫ 59cos(u)  du…

Q: Evalate jsinty)hube where 2 05ys1,05xsy. a) 1-cos(r) b-costr)) 9-cosd) osd) d) 1-cos(l))

A: Change of variables:             ∫x1x2∫y1y2f(x,y)dy dx=∫y1y2∫x1x2f(x,y) dx dy.

Q: 7/4 27/3 Evaluate the iterated triple integral S S Se sin(y) dp dy do. Present the answer as a…

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Q: Evaluate the integral i.) 2 S² S₂y ez dxdy हैं,

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Q: 11 Let I= [[5 sin(v')cydx . By reversing the order of integration of I, we get:

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Q: The suitable substitution to evaluate the integral (V cot (2x) dx is sin (2x) Ou3tan(2x) none Ou=…

A: To find The suitable substitution to evaluate the integral.

Q: z'e? dz

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Q: 13. compute the integral // e10(x-y)²+8zy dædy over the ellipse & := {(x, y) ; 5x² + 5y² < 6xy+ 1}.…

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Q: aluate the integral / (8 x + 18y)dx + (24x – y)dy alor y = x² from (0, 0) to (1, 1). TE: Enter the…

A: Topic:- application of integration

Q: aluate the iterated double integral. 1 cos(y) /5 + cos² (y) dydx Saresin (2)

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Q: Compute the integral VI-y² In(a? + y? + 1)dædy 1-y² y=-1 Jr= and enter the solution below with up to…

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Q: 17 z cos(8 z) dz Which of the following choices of u and du are consistent with the principle of…

A: Solve the integral using integral byparts

Q: If | h(2)dz = 4 and | h(2)dz = 9.1 %3| 1 what does the following integral equal? |h(2)dz = 4

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Q: [4] 5. Use the fact that 1 +C 4e2r dx = 2e2 to either evaluate the improper integral 2 dr, or show…

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Q: Evaluate the integral fo S (y co W COS + 2) dydx.

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Q: Evaluate the integral. 1 8 dt V15-21-? - 1 OA. 6 В. O C. 4 D. 3" O D. co fm

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Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: 15. The area enclosed by r=2– 2 cos 0 is: А. В. С. 9Tt/2 D. 9t/4

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Q: Evaluate the iterated double integral 2 b.) √ √ ² sinπTy ³ dydx

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Q: 1 x²y dy dx 2 Jo /0 Jo

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

Q: (3) Using Hilbert-Schmidt theorem, solve the following integral equation: (1) y(=) = (x+2)*+ /…

A: Given integral equation, yx=x+22+∫-11xt+x2t2ytdt          ...1 Here fx=x+22, λ=1 Firstly find the…

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.