Q2 ) Evaluate the integral S*9/x7 + y²) dxdy.

Q: Evaluate the integral J dx V4-9х2 3.

A: This question is related to integration.

Q: Evaluate the integral. * T/3 3 sec 0 tan 0 de In/4

A: Given that the integral is ∫π4π33secθtanθdθ. It is required to evaluate the given integral…

Q: Evaluate the integral. 7y 1-7y dy

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Q: Evaluate the integral fa*(2* – 2)" dz 15 by making the substitution u x4 – 2. -

A: Given : ∫x3(x4-2)15dx

Q: Evaluate the integral f 2x (x² + 6)° dx using the substitution u = x2 + 6. | 20(x² + 6)* dzx +C

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: Let a, b> 0, then the integral x2a +1(1-x²)bdx, after changing variables y = 1– x will be expressed…

A: Given the integral I = ∫01x2a+11-x2 b dx To changing variables y = 1-x2 will be express

Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

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Q: Evaluate the integral. 10 sec 2(5t) dt J7+2 tan (5t)

A: We have to integrate the  I=∫10 sec2(5t)7+2tan(5t)dt

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: Use Green's Theorem to evaluate the integral 3x²y²dx + (5y³ – x³y²)dy, C

A:

Q: Evaluate the integral +2 zp; :- 2 in the two cases: 1) y = {z :|2| = 1}; 2) y = {z : |2| = 3}.

A: We will evaluate it by Cauchy Residue Theorem Let R be the residue then ∫f(z) dz = 2π i R Firstly,…

Q: Graph the integrand and use geometry to evaluate the integral. 6 2) s V36 - x2 dx -6

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Q: Compute the integral of f(x) = 0.4 – 2x² + 40x5 from a = 0 to b = 0.8 using i. Trapezoidal Rule with…

A: Numerical integration

Q: Evaluate the improper intergal 1 dx using the residue (x² + 16)² theorem.

A: We need to evaluate integral.

Q: Evaluate the integral f 2x (x2 + 7)° dx using the substitution u = x2 + 7. 2.x (x² + 7)° dx +C

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Q: Evaluate the integral. 4 | VE(6 + 2t) dt

A: use distributive property on function and integrate it.

Q: Evaluate the integral f 2x (x² + 3)° dx using the substitution u = x2 + 3.

A:

Q: Evaluate the integral. 7 √49-x² √49-x²-22 49-x² 1 √²-3³ (x² + y² + 2²)1/2 dy dz dx =

A: Solution:-

Q: (4 b Prove that 5 foxx dx = K (6-a) using definition of integral, where fø= k [a,b], on

A: Given function is fx=k on a,b. We have to prove that ∫abfxdx=kb−a. Take Left hand side  Use Property…

Q: 2. Use Cauchy's Integral formula, Evaluate the following • I= sin4z ,IZl= 3

A: I am attaching image so that you understand each and every step.

Q: Evaluate the integral 3 -x a. So Sox² exy dydx 0

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

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Q: 9. dt 2 -4

A: ∫9t2-4dt=9·∫1t2-4dtLet u=\arcsec12t=9·∫secudu=9lntanu+secuSubstitute back…

Q: The improper integral 5dx is V1-x?

A: Since you have asked multiple, we will answer the first one. ∫015dx1-x2dxLet x = sin θ ⇒ dx = cos θ…

Q: y = sech*x = In(_+ V1- x², sechx = In(- 1+ V1-x² Prove that .... ..

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Q: Evaluate the integral į (1 – x– 4x° + 2x*)cx using multiple-application trapezoidal rule with n = 2

A: Given, fx=1-x-4x3+2x5 The trapezoidal rule to approximate the area:  ∫abfxdx≈∆x2fx0+2fx1+2fx2+2fx3+.…

Q: Suppose that f and g are integrable and that -1 f(x) dx = 5 h(x) dx = 4 7, dx = %3D Use the rules to…

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Q: Evaluate the improper iterated integral. • 1/x9 y dy dx Jo

A: In this question we have to evaluate the integral.

Q: 15. S(x + 2)²dx

A: Solve the following

Q: Evaluate the integral. 2 | 7t sec -'t dt 2113 | 7t sec - 't dt = 2113 (Type an exact answer, using t…

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Q: Consider the integral 2 6z² In(z) dz

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Q: Evaluate the integral

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Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: Use the Trapezoidal Rule to evaluate the integral fx-¹dx. 1 2|3 NIC 34 2

A: We have to evaluate the integral ∫12x−1dx by using the trapezoidal rule. Here, a=1 and b=2 And…

Q: Evaluate the integral. 2 - 121 y - 121 2 -dy, y> 11 dy=

A:

Q: 3. Evaluate JIJ 62² dV where G is bounded by x + 2y + 4z = 8 in the first octant.

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Q: Evaluate the integral. inegral  ax / (x2 - bx ) dx

A: Consider the given integration as I=∫axx2-bxdx⇒I=∫ax-bdx

Q: Evaluate the integral. 4 2t 9 -i- j+¬Vt k dt (9+?)*

A:

Q: Evaluate the integral. 2 (8t i - j+ 3t5 k) dt

A: We first separate the integral

Q: Evaluate the integrals

A: Given information: ∫141ti+15-tj+12tkdt

Q: Use the Trapezoidal Rule to evaluate the integral S |r| x²dx O 2 O -2 O 1 -1

A: Given Intergral ∫-11xx2dx. We have to find the value of it by using the Trapezoidal Rule. The…

Q: v) ₁ √√¹-x² sin(x² + y²) dzdydx fő

A: Given is  ∫01∫01-x2∫01sinx2+y2dzdydx In order to solve this integral it is needed to first convert…

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

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Q: Evaluate the iterated double integral. I 3 3y be dady A

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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: Evaluate the integral dz dy dr. -2 Jo 5-722-7y2 32

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Q: Evaluate the integral: –(9z²+7x) dr %3D (1-1)(z+1)²

A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

Q: Evaluate the Integral Sec² √r √x dr Njw SYD

A: Given: ∫1832sec2xxdx To find evaluate the given integral.

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.