Q2. Use integration by parts to evaluate the following Integral 2 COs x² dx

Q: A. Evaluate the following integrals. 1. S(Vcos x + sin x)´dx 2. S cos³ 3x dx 3. S tan5 2x dx

A: To evaluate the following integrals.1 ∫cos x+sin x2 dx2 ∫cos33x dx3 ∫tan52x dx

Q: |(x² + 2x) cos(2x) dx

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Q: Q3/ Evaluate the integral: TT ° cos(x²)dx dy

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Q3. (30pt) Calculate the integral 2x³ – 4x + 1 - (1– cos x) dx 1+x? a) for n= 10 according Simpson…

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Q: Q2 – Evaluate the following integrals. i. S(sin(4x) + cosh(3x))dx

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Q: Q1: Evaluate the following integrals by substitution dx 1. e cos e*dx dx 3. J 2x- 3

A: Solve by substitutions

Q: Q3/ Evaluate four of the following integrals. ( x³+1 sinx cosx dx b. f*+¹ dx c a. S √1+cos2x x²

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Q: Evaluate the following double integral (x² cos y – sin x)dxdy. 0.

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Q: Evaluate the integral [e2 cos(2x)dx.

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Q: Find the integration of the following   x2 / x sin x + cos x

A: Our Aim is to integrate the following expression given below:-x2x sin x+cos x -(i)

Q: Determine the following integrals: I. In x dx II. | a? cos(2r) dx III. cos° x dx

A: As per our guidelines, I can answer maximum three subparts of a question. Since you have asked for…

Q: 1. Evaluate the following multiple integrals: 2 252 cos y dædy

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Q: Evaluate (3 t + 5) cos () d+ using integration by parts .

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Q: Q2 Find the integral for the following : 2- fe-*sec? (ne-*)dx dx 3- JItex dx 1-S; 2x+2x

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Q: Evaluate the integral 7ª S* (y cos x + 4) dydæ.

A: The detailed solution is given below Thank you

Q: Evaluate the following Integrals 1 I. dx 1-cos x

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Compute the following integrals: sin x dx -T/2 :/3 |(cos x)(sin? x) dx -n/3

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Q: Determine the following integrals (a). cos xsin.xdx (b) [- dx 17-5x+6 (c) fxe*dx

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Q: The suitable substitution to evaluate the integral V cos (2x) dx is COS

A: Given that:∫cos5(2x)csc3(2x)dx

Q: Evaluate the following integral. ex cos(x) dx

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Q: 2 X COS x dx ах

A: To integrate: ∫0π2x cos (x) dx

Q: Evaluate the following integrals TC 2x a) -e + sin dx V3x 0. 3. cot(-2x) csc?(-2x) dx b) 7.

A: (a) I=∫0π53x-e+sin-2x3dx =∫0π53x dx-e∫0πdx+∫0πsin-2x3 dx  ∵∫(u+v) dx=∫u dx+∫v dx…

Q: c) Evaluate the following Integration by parts for definite integrals. -5x dx хе 3 ii) . 2 Sin-dx i)…

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Q: Q1. Evaluate the following Integrals 1 dx 1- cos x .2 +x - 2x +3 dx

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Q: Which of the following integrals are improper? (Select all that apply.) dx 5х — 1 dx 2х — 1 sin(x)…

A: An improper integral is a definite integral in which the limits approach a constant, or,…

Q: A. Evaluate the following integrals: 1. sin 'xcos x dx

A: Given: I=∫sin7xcosxdx   ....(1)   We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Evaluate the following integrals S, 5v – 3) (e-y*2 sinhy) dy а. b. 8(x + 1) In(sinx2*) cosx dx

A: We have to define the given Delta function and find the points in which it is non zero in the given…

Q: Evaluate the integral. x2 cos(7 x) dx +C

A: The given integral is: I=∫x2 cos(7x) dx

Q: a) Evaluate the following integrals 1) xe3*dx 2) | x2 sin x dx 3) | x sin 2x dx

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Q: 5. Evaluate the integral: Jsin?x cos'x dx

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Q: Evaluate the following integrals.

A: To integrate: ∫0π2e-3xcosxdx Use integration by parts:      ∫u dv = u v - ∫v du Let   u =cos(x)…

Q: Evaluate the following double integral (x², coS y – sin x)dxdy.

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Q: 1. Evaluate the following integrals. ? cos(r) dt а. Зx2 — 1 dx b.

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Q: (a) Evaluate the following integrals: π cos(x) dx dy 4y

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Q: 1. Evaluate the integral: (a) cos(x) dx dy 4y

A: the given integral is: we have to evaluate the given integral.

Q: Evaluate the given integrals 1 -dx b. Į S7-2 cos x

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Q: Evaluate the following integral. TC - -4x coS x dx

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Q: Evaluate the multiple integral cos(x - y) dx dy

A: Here we have, I=∫11+π2∫1ycosx-ydxdy

Q: 1. Evaluate the following integral: Sx? sin x dx

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Q: Evaluate the integral. | Te" cos(2x) de = 7e* cos(2x) dx +C

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Q: 9. Calculate the following definite integrals by hand. (a) x² + 4x dx (b) cos(x) dx (c) o JE 3 dx

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Q: Evaluate the given integral. *2x 2ye-X dy dx Jo

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Q: Evaluate the given Integral 1. ſ csc x (cos2 x - 1)dx

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Q: b) Evaluate each of the following integrals: 2 i) | cos(2x)dx, 4x3 -dx. 1+ x* ii)

A: Explained below

Q: Evaluate the following definite integrals. (а) |2t – 4| dt. /- (b) cos(3x) dx. (c) d.x.

A: You must have an idea about definite integral to solve these questions. In these types of integral…

Q: [9 cos (12 – 6t +1) dt 4

A: Solved below

Q: Evaluate the following integrals. Tt/42 cos x dx e* 2 cos а. S dx V1-9x²

A: We have ∫0π42 Cosx dx Now, ∫0π42 Cosx dx becomes  ⇒2Sinxπ40                         as ∫Cosx…

Q: Determine the following convolutions by integration (a) 1 * sin wt (b) et * e

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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.