Q2) Evaluate the integral x3 dx 3 a *0.

Q: Evaluate the double integral. LL. 3 (x² – xy2) dy dx -3

A: first, we integrate with respect to y

Q: Evaluate the improper integral 2x dx, if it exists. (x² + 81)2

A:

Q: 5. Evaluate the integral 2 c2x x2 (x² + 2y³) dy dx.

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: Evaluate the integral dx (3x + 15)²’ by making the appropriate substitution: u = dx + 15)?

A: To evaluate:∫dx3x+152

Q: -1-y 3) Evaluate the integral dxdzdy?

A:

Q: Q2:A/ Evaluate the integrals 1 sec²(eVx + 1) dx J Vxe-V

A: Given: ∫1xe-xsec2ex+1dx Consider, u=ex+1, du=ddxex+1=ex+1ddxx+1=ex+12xdx

Q: 3 Calculate the integral: dx x² V25 + x2

A: Here first put x=1/t and then the expression inside the square root as y^2. As showing in solution

Q: Evaluate the integral. HINT: 3 x2 dx J2 x - 1

A:

Q: Evaluate the integral.

A: Given integral: ∫121241-x2dx

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

A: We need to evaluate integral.

Q: Evaluate the improper integral 2x dx, if it exists. (x² + 81)² 8.

A: The value of the integral ∫-∞02xdxx2+812 is given by: ∫-∞02xdxx2+812=-1x2+81-∞0=-181-1-∞=-181-0=-181

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

A:

Q: Evaluate the double integral 2. dy dx 3/x

A:

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: Evaluate the integral (2a+4)(x² + 4x + 2)*dx 4 by making the substitution u = x+ 4x + 2. ,2

A: Let u=x2+4x+2, now differentiate it with respect to x. du = (2x+4)dx So,…

Q: (a) Evaluate the integral 1 2 (4-)dy dx

A: Evaluate the given integral as follows. ∫01∫024-y2 dy dx=∫01∫024-y2 dy dx=∫014y-y3302 dx=∫018-83…

Q: Use the specified substitution to find or evaluate the integral.

A: Consider the provided integral, ∫01 dx23-xx+1 Evaluate the provided integral. ∫01…

Q: Q2:A/ Evaluate the integrals sec (1 + ex) tan (1 + e'/x) dx

A: Integral

Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

A:

Q: 3 Evaluate the integral |x V2x +1 dx ?

A: ∫x22x3+1dx We need to integrate the given function.

Q: a) [ Evaluate the integral 4x - 1 (x + 2)(2x - 1) S -dx.

A:

Q: Use the substitution formula to evaluate the integral. Vx +1 dx B) 2/2 - 1 D) 3/2 - 3

A:

Q: 2e Evaluate the integral dx 2x +3

A:

Q: Use the substitution formula to evaluate the integral. fin-√3/22 c2x dx 1 + e4x 28) 0

A:

Q: evaluate the integral.

A:

Q: Evaluate the integral. dx J2 (x² – 1)3/2 -Csc O

A:

Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C…

A:

Q: 4. Use residues to evaluate the improper integral 1t r4 a + x2 dx; where a is a real constant.

A:

Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: Q1)Evaluate the following integral: 2 1-x dx 1+x2,

A: 1 We have to evaluate the integral ∫021−x1+x22dx. Now,…

Q: Evaluate the integral dx (4x + 14) by making the appropriate substitution: u = dæ (4x + 14)* Submit…

A:

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

A: Solution:

Q: Evaluate the integral dx (2x + 6) by making the appropriate substitution: u = dx (2a + 6)°

A: To evaluate the given integral.

Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: Evaluate the integral Зx2 — 4х — 9 A В + C dx using x3 – 2x2 – 9x + 18 - 2 x +3 – 3* х — х — 3x2 –…

A:

Q: Evaluate the integral dx (2x + 4)* by making the appropriate substitution: u = dx (2x + 4)°

A:

Q: Evaluate the integral. dx i. 2 x²Vx2–1°

A:

Q: Evaluate the double integral dy dx 4. 2.

A:

Q: Evaluate the integral 2x (x2 + 3)° dx using the substitution 6 u = x + 3. | 2.x (x² + 3)° dx +C II

A:

Q: 7. Evaluate the integral. Vx2 – 25 dx х3

A: First we will make a trigonometric substitution of x=5*sec θ then we will solve it and integrate it.…

Q: ग Use the Midpoint Rule to evaluate the integral fx sin(x)dx. D]2 co | Fo 프2 NN

A:

Q: 10 Evaluate the integral f 2x (x2 + 4) " dx using the substitution u = x² + 4. 2x (x² + 4)*" dx =|…

A: The given integral ∫2xx2+410dx

Q: Evaluate the integral. 9. dx J2 (x² – 1)3/2

A:

Q: Evaluate the integral. 10 r FIL √16 22 1 (x² + y²) 1/2 dy dx dz =

A: To evaluate the integral ∫04∫-44∫-16-x216-x21(x2+y2)12dydxdz

Q: Q1-Evaluate the integral 2х — 5 dx - х2 — 5х + 1 3

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

Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate:

Q: Evaluate the double integral : 9 dy dx 36 – 12 - 12 -36

A:

Q: Evaluate the iterated integral. 2 4 (x2 – 2y2) dx dy 1 Jo

A:

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.