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

Q: Use symmetry to evaluate the following integral. 2 ja (2- |x|) dx - 2

A:

Q: Evaluate the integral. dx :+ C J 22 Va2 – 36 x² /x? - NOTE: Enter the fully simplified answer with…

A:

Q: Transform the integral fo o sin o sin 0 do de by the substitution x = sin o cos 0, y = sin ø sin 0…

A: Solution: The given integral is I=∫0π2∫0π2sinϕsinθdϕdθ The substitution is x=sinϕcosθ, and…

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: Evaluate the integrals in Exercises  by making a substitution(possibly trigonometric) and then…

A: since you have posted multiple questions so I'll solve first one for you , for rest question's…

Q: Consider the integral dx . Using u-substitution, what is the appropriate u and du? -2x 3e 2t 2e

A:

Q: Express the integral in terms of the variable u, but do not evaluate it. In c dr; u = In x rels In c…

A: To determine: where  u = lnx

Q: Given the integral " Se F(x, y) dydx, which ONE of the following integrals is equivalent?

A:

Q: Use contour integration to compute the following integrals. (a) 1. 2π cos(20) dv 5+4 cos v

A: (a) Given integral ∫02πcos(2ϑ)dϑ5+4cosϑ. The objective is to compute the integral by using contour…

Q: 'ind the line integral of F(x, y) = (x² – y² , 2xy) = (P, Q) along the boundary of the rectangle %3D…

A:

Q: Evaluate the integral by making the given substitution. sec(6z)tan(6æ)dr, u = 6z + C

A: According to question given :∫sec6xtan6x dx, u=6xWe have to evaluate the integral by making the…

Q: Evaluate the integral da 2+ et using the substitution u = 2+ eª. dx 2+ et +C | -

A:

Q: Write other flve iterated integrals tiat are egual to rf (x,y,z) dz dy dx GOMAGE

A:

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

A: Given,          ∫π2π6coszsin5zdz

Q: Evaluate the double integral /| (2² + 8y) dA, where Dis bounded by y = x, y = x³, and æ > 0. Answer:

A:

Q: Evaluate the integral 24 11) dx, by making the appropriate substitution: u = Ja* (2* – 11)*“dz =

A: ∫ un du =un+1n+1+C

Q: Evaluate the double integral. 8ху? dA, D is enclosed by x = 0 and x = 4 – y2

A:

Q: Evaluate the integral by making the given substitution. [sec (3x)tan (3x)da, u = 3x +C

A:

Q: Evaluate the integral 20 | by making the appropriate substitution: u = 5 – 2 (2³ – 2)® dx %3D -

A: Evaluate the integrals

Q: Find the anc length oF t1x)=x° on [o,] Hint; use the Integral Tables,

A:

Q: Use an appropriate contour integral to evaluate the following real integral rinfinity (26 – 8)dx Jo…

A: Given, integral is as, ∫0∞x6-8x4+5x+42dx  I=12∫-∞∞x6-8x2+12x2+42dxconsider…

Q: Evaluate the integral using FTC I.

A:

Q: Evaluate the integrals:

A: Integration: ∫sect dt=ln|sec t +tan t|+c∫u.v dx=u.∫v dx -∫[ddx(u).∫v dx]dx   [ by parts]

Q: Evaluate the double integral x cos y dA, where D is bounded by Y = 0, y = x², and x - 2. Answer:

A:

Q: Use this result to either evaluate the improper integral +oo 5xe dr or show that it diverges.

A:

Q: Consider two integrals: (b) S, x³dx Where a, B> 0 are both positive real numbers. Given that a < B,…

A: In the question we have to determine which integral is larger.

Q: Evaluate the integral f 2x (x² + 2)° dx using the substitution u = x? + 2. | 20(a* + 2)" de +C

A: The given integral is: I=∫2xx2+26 dx

Q: b) Given UTMUTM VI+ approximate the integral using trapezoidal rule with h = 0.25. dr, UTMUTM

A:

Q: Evaluate the integral. 'Tt/2 7 cot (x) dx T/4

A:

Q: Evaluate the integrals LI Vy+I dy b. So a. 5r dr (4+r²)?

A:

Q: Finel the integraL of finchio XSina) wher ne 5 and (0,2) by Simpsors rule 3.

A:

Q: 1- Assume that x, y € R and z = x + iy € C .Calculate the following integrals using the given…

A: a) Given ∫0∞lnx1+x2dx ∫0∞lnx1+x2dx=12∫-∞∞lnx x-ix+idx=122πi Resi=πiln i2i=π2ln i=π2ln1+π2 i=π20+π2…

Q: Evaluate the double integral æ cos y dA, where D is bounded by y = 0, y = x², and a = 1. Answer:

A: Solve the following double integral

Q: Calculate the integral Sa-ydA D where D = {(r, y)|0 < < 2y < 2}. %3D

A:

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: Use the substitution formula to evaluate the integral. , π/2 20) cot x csco x dx T/6

A: on solving this we get

Q: Evaluate the integral by making the given substitution. sec(4x)tan(4x)da, u = 4x + C

A: To find following integration  I = ∫ sec(4x).tan(4x).dx

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

A: We will evaluate the given integral as shown below

Q: Evaluate the triple iterated integral. T/2 r cos é dr de dz Jo

A:

Q: By using Simpson's Rule, calculate the integral 2r +a?dr.

A:

Q: x2 dx 3. (бх2—49)"/2 49 [V36x3-9x IVox + v6x2 –9 + In + C I 12v6 49 7

A: In this question we will use basic of calculus i.e concept of integration. We will simply use…

Q: Evaluate the integral using the given substitu Sxcos (5x?) dx, u=5x? dx, u= 5x sin (5x?) +c О в. sin…

A:

Q: Use the Residue Theorem to evaluate the a? integral dx + x2 where a>0

A:

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

A:

Q: (24 — бх) dx 14

A:

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

A:

Q: In evaluating the inte gral, Substitution leads to a now integral S f(u) du xST+2x dx 1 Correct for…

A: Given∫012x21+2xdx

Q: 1. Evaluate the integral: , xe*+y* dV where B is the portion of the unit ball x? + y? + z? <1 that…

A:

Q: Evaluate the integral by choosing a convenient order of integration: x cos(xy) cos' (Tx) dA; R 0, x…

A: Given

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.