1. Evaluate the integral. S. a) t sin3tdt b) / V1+a* dx

Q: 4. Evaluate the following integral using three-point Gauss-Legendre quadrature: 3.5 dx Vx2 - 4 3.

A: We will use the three-point Gauss-Legendre quadrature. First we convert the given integral…

Q: Write the integral S Li dz dy dx in the form dx dy dz. Do NOT evaluate the (2) integral.

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Q: dx Evaluate the improper integral x(In x)?

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Q: Evaluate the fo llowing integrals S Sin () dx

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

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Q: a) Evaluate the integrals using appropriate substitutions. dx Sino i)S i) f de Cos? 8+1 1+16x2

A: as per our guidelines I am solving only first question with both parts a(i) ∫dx1+16x2ii ∫sinθcos2θdθ

Q: Evaluate the integral / cos[3 +1/(z – 3)] dz, where Y is the unit square with corners at 0, 1, 1+i e…

A: Given; ∫γcos3+1z-3dz Where, γ is the unit square with corners at 0,1,1+i e i

Q: 4: Use Green's Theorem to evaluate the following integral e dx + (5x+ 6) dy Where C is the triangle…

A: Using green theorem to evaluate the following integral.

Q: Evaluate the integral. * m/6 cos(z) dz sins (z) Jn/2

A: Given,          ∫π2π6coszsin5zdz

Q: Evaluate the triple integral S" S, sin y² dz dy dx.

A: We need to find the triple integral ∫03∫0π∫0ysiny2dzdydx. So,…

Q: Evaluate the iterated integral. T/4 1 Tv cos(x) dy đx

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Q: Evaluate the iterated integral. 1 1I 11ze- dx dy dz O Jo Jo

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Q: Apply Cauchy integral formula to find the value of the integral ſ. AG-DE dz; where C: |z| = 3. 2z-1

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Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h=; , to approximate the integrale-2x²…

A: Note:- As per our guidelines, we can answer the first part only as both are different and first part…

Q: 1- Find the integral of: 2 cot - de T/2 A- B- / dr Vr

A:

Q: 2. Compute the following integrals. tan"(2) sec"(r) dr. (b) sin*(x) tan(x) dx.

A: (a) given that a integration of tan3(x) *sec6(x) Here we compute this integration. We know that tanx…

Q: Evaluate the iterated integral. TT V4 – z² z sin(x) dy dz dx

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Q: The result of the integral in 0 given 25 dy is 5 tane - 50 +C, y A True False

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Q: Evaluate the integral of (3x + 9y) dx dy, use the inner limits from 0 to y and outer limits from 0…

A: Given: The double integral ∫∫3x2+9y2dxdy, here the inner limits varies from 0 to y and outer limits…

Q: evaluate the triple iterated integral.

A:

Q: Evaluate the integral b. 0 (z sin x + z cos y)dzdydx

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Q: Evaluate the donble integral dy dx

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Q: Evaluate the integral (t³ In ti+ 3t³ sin (t) j+k) dt.

A:

Q: Evaluate the integrals: A: So So x sin y dy dx

A: ∫0π∫0xx siny dy dx

Q: Evaluate the integrals in ∫7cos t sin t dt

A: Given Integral,I=∫7 cos t sin t dt

Q: DEvaluate the double integral x cos y dA, where D is bounded by y = 0, y = x², and x 2. %3D

A: Integration of cos(x) = sin(x) Integration of sin(x) = -cos(x)

Q: Compute the integral fo S x cos(xy)dxdy

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Q: Calculate the iterated integral o L? 5x cos y dydx

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Q: Sye-y*dy

A: The value of the given integration can be found with the help of the substitution. Substitution of…

Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: 11. The integral of nunex dx is bln]sec(In(2x)")|. What is b? A. 2 B. 2 C. 4 D.

A:

Q: Evaluate the integral cot2x dx J Tcot?x – 15

A: We will evaluate the given integral as shown below

Q: The resulting integral of S dx is In + e Tan"1+ C where a, b, d, and e are integgrs. x+x²+4x+4 What…

A: Differentiate the result of the integral:…

Q: Evaluate the integral S (* In ti+ 3t sin (t*) j+ k) dt. x(*+1)

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Q: Apply trapezoidal and Simpson's rules to the integral 1 =[ \1-x² dx h=0,2

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Q: /2 TT Sin (x ty) dy dx 0

A: Consider ∫0π2∫0π2sin(x+y)dydx = ∫0π2∫0π2sin(x)cos(y)+cos(x)sin(y)dy dx =…

Q: 4. Evaluate the following integral using three-point Gauss-Legendre quadrature: 3.5 dx Vx2 – 4 3.

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Q: 2. Approximate the following integrals using Gaussian quadrature with n = 1 and n = 2. 1 1 2 -dx 4…

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

Q: Evaluate the following integral: J Sec?x -dx V1-tan2X

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Q: Evaluate the Integral 3. TT T y Cos z dx dy dz

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Q: /2 etan y sec y х cos" ydxdy

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Q: The result of the integral in 0 given V Vr²- 25 -dy is 5 tan0 -50 +C, True B False

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Q: Which of the following integrals represent the area enclosed by the smaller loop of r = 1 +2 sin 0?

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Q: Compute the integral | x"dx, with a=1, b=7, and N=5. Answer to three decimals.

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Q: In Evaluate the integral: Sto st² sin s teu du ds dt

A: The given integral is: I=∫12∫tt2∫0lnsteududsdt   The Power Rule: ∫ax+bndx=ax+bn+1an+1+C

Q: 7/2 VI- cos z dy dx dz

A: The detailed solution is as follows:

Q: 4. Evaluate the following integral: Se-y cos y dy

A: Solve by integration by parts.

Q: . Evaluate the integral S (t* In ti+ 3t sin (t*) j+ ) dt. +1)

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.