In2 Evaluate the iterated integral ſo"" S 7 dxdy

Q: Evaluate the integral. In 2 2 e sinh 0 d0 - In 10

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Q: In evaluating JxVx-2 dr þy substitution, if u =x- 2 then what will be the resulting indefinite…

A: Explanation of the answer is as follows

Q: Evaluate the integrals. Show all work. 1. 0 cos (T0) de 1/2

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Q: 2ェ dr Vェ? +1

A: We have to find the given integral.

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫e3x + 1 dx

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Q: (b)Evaluate the integral directly we-wdw

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Q: Q1/ Use Gauss-Legendre formula to evaluate the integral o e-dx withn= 3.

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

Q: Evaluate the integral: Jo Sí(3xyY+ 5) dy dx Answer:

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Q: Evaluate the iterated integral I = SoS(6,? + 8x) dxdy

A: Solve the following

Q: evaluate the integral fromn 0 to pi/2 (cosx)^3

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Q: Find the indefinite integral. | (0.9t² + 0.06t + 2) dt + C

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Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫(x + 1)12…

A: Given: ∫12x+1dx for evaluating this integral we substitute u=x+1 now differentiate both side with…

Q: Use a substitution of the form u = ax + b to evaluate thefollowing indefinite integrals.∫ cos (2x +…

A: ∫cos2x+5 dx Now put 2x+5=u Differentiating with respect to x, we get 21+0=dudx⇒2 dx=du⇒dx=du2

Q: 6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12…

A: Let's find.

Q: Evaluate the given indefinite integral. Indicate u, n, and du. Scos" }y sin ydy

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Q: 21. Write the definite integral that repre formed by y = x² + 2x + 1 and y=2x+5. Do:

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Q: Make the given substitution to evaluate the indefinite integral. 28r dr .u= 3-r 3-r'

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Q: 1 4. f₁² (1-x²) dx 5 2

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Q: TU 8. fz sin¹x cos5 x dx 2 0

A: To find the value of the given definite integral:∫0π2sin4x cos5x dxWalli's Formula:∫0π2 cosnx dx=…

Q: Q.5 Evaluate the integral with the aid of the formulas 5,6, and 7. dt 9-4t2

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Q: TU 5.fo cos³ 30 de

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Q: TU f2 sin² p cos6 p dp

A: Solution is given below:

Q: dydr 13. Evaluate the double integral J, J, o x²+7 a, In 10 b. In 10-In 7 а. c. In 11 d. In 11+In 7…

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Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

Q: 1- Find the integral of: A 2 cot - de 3 T7/2 А-

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Q: Evaluate the integral 0.8 x · In(6 sin r) dæ.

A: Let us assume: u=6sinxdu=6cosxdxcosx·dx=du6 At x=0.2, u=6sin(0.2) At x=0.8, u=6sin(0.8)

Q: Q.5 Evaluate the integral with the aid of the formulas 5,6, and 7. dt V9-4t2

A: We have to solve integration .

Q: Sy² sin(3y³ + 4) dy

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Q: +00 dx Evaluate the improper integral x(In x)²

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Q: A. Evaluate the integral of the follo x+4 1. dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Q1/ Solve the following iterated integral: SL. ex-ydA, R: 0sxs In 2, 0sys In 2.

A: 1) We have to solve the iterated integral ∫∫nR ex-ydA where R= 0≤x≤ln2 ,0≤y≤ln2

Q: 10. | Vi(1? + 31 + 2) dt

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Q: Evaluate the given indefinite integral. Indicate u, n, and du. Scos* y sin ydy

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Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ t dt/t4 - t2 - 2

A: Let's obtain the partial fractions:

Q: Find the indefinite integral. 5. 3 dt 12 +C

A: Formula: ∫(1/x) dx =lnx ∫xndx = xn+1/n+1

Q: d) Determine the infinite integrals of the following e+2 i. ii. 2 3 sin2x dx

A: Evaluation of the integral

Q: Evaluate the given indefinite integral. Indicate u, n, and du. [5lan2P etan 28 sec² 2 Bd ß

A: Let I=∫5tan2βetan2βsec22β dβ

Q: Consider the following. 9. dx x2 + 18 (a) Evaluate the integral with the Fundamental Theorem of…

A: The solution are next step

Q: Find the general indefinite integral. √ (9 -1) (4 +1²) dt

A: Solution of given question is written in below steps.

Q: TU 2. fz sin² x cos4 x dx J

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Q: Evaluate the integral from 0 to 1. 3/(1+t2)j + 5t4/(1+t5)k

A: We first separate the integrals. ∫3(1+t2)j+5t4(1+t5)kdt=3∫11+t2dtj+∫5t4dt(1+t5)k=3arctan(t) j +…

Q: Evaluate the integral. r3 3 cosh(t) dt 30.05

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Q: Express the integral L Ey.2) dadrdy as an iterated integral in the other five different ways.

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Q: Evaluate the improper integral dz, if it exist (x² + 49)2

A: Here we have to evaluate the given improper integral.

Q: 14. VE (t² + 3t + 2) dt

A: We use the formula integration of xn dx=xn+1/(n+1). See 2nd step.

Q: Evaluate the integral.   The integral from 1 to 4 of e^(4/x)/x^2dx

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Q: Q3. Evaluate the following Integrals Stan* 0 sece de I. 2-16 хр- Vx II.

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Q: Find the general indefinite integral.   ∫ (u +4)  (2u +1)   du

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Q: Evaluate the integral of ax^2 e^bx dx assume a and b are constants.

A: Please see the explanation below

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.