Evaluate the following integrals. 3xx + 1dx b. de. a. tan²

Q: Evaluate the following integrals using the appropriate technique. dx (a) S (b) Sp5lnp dp 5-3x

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Q: Evaluate the following integrals- dx x(Inx)((Inx)2-3lnx+2)

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Q: Se*cos2x dx

A: We have to evaluate the integral ∫ex cos(2x) dx.   Integration by parts : ∫u·v dx = u·∫v dx -…

Q: Evaluate the following integrals.

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Q: Evaluate the following Integral: b. Sx³Vx? +1+ 9R) dx

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Q: Which of the following integrals are improper? (Select all that apply.) dr 8r dr 2.x p sin (x) da…

A: First I have written a note, which tells about the improper integral , just use the definition of…

Q: Evaluate the following integrals r0.5 S"x cosh(x² + 1) dx

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Q: Evaluate the following integrals (i) So V1– cos 2xdx

A: Since there are multiple questions posted, we will answer the first one (i). If you want the…

Q: S In x dx

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

Q: Evaluate the following integrals. Show all the necessary solutions. 2. y In?(1 + 3*) dy 1 + y²

A: I=∫y ln7(1+y2)(1+y2) dyI=∫ y ln(1+y2)7(1+y2) dyln(1+y2)=t1(1+y2) (2y) dy =dty(1+y2) dy=dt2

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Q: Evaluate the following integrals. xdx |Ja +3 а. b. z · 3*dz | VI (2 – x)² dx с.

A: Let's find.

Q: Evaluate the following integrals: 4T Vcsec 0 de 0

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Q: Evaluate the following integrals.  Z sin^6 (2x) dx

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Q: V. S, sin* () cos5 (-) dx

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Q: sech?x ix. xp: tanh(x)V1-tanh²x

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

Q: Evaluate the following integrals. Jo cos?

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Q: vi. S cos(3 Inx)dx

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Q: Evaluate the following integrals i) / Vỹ++edy 3. Vy

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Q: Evaluate the following integrals.

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Q: J xcos xdx 2. -3x J

A: Note: As per company policy we are supposed to solve only 1 question. So, kindly repost other…

Q: Evaluate the following integrals Sa 4 |(x? + 4vz - - 6)dx x3

A: To solve integration of such type. You just need to integrate individual terms separated by either +…

Q: 1 8. 3 cosº x/2sinx

A: Integration of function expression under certain limits give the value of area between function…

Q: cosx dx Vsin? x-2sinx-3

A: SOLUTION-

Q: - sec (r)) de 3a sin(r+5) da

A: Integrate

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A:

Q: Evaluate the following integrals. (a) / ( + 3x) sin(z)da

A: a) The given integral ∫x2+3xsinxdx Use integration by parts, let 1st function be x2+3x and the 2nd…

Q: 2dx Jo 2x²+3x+1

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Evaluate the following integrals: - TVī + vi csc(t) (a) dt

A: The given integral,∫t2-πt+t csc(t)tdt

Q: Evaluate the following integrals: | VE(x +1) de:

A: Given:       ∫xx+1dx     =∫xx+xdx        =∫x32dx+∫x12dx

Q: 2z -dz l|z||=10 ПЕ-10 (2 — 1)(2+ 1)

A: NOTE: The closed curve will be denoted by z=10 because it is a circle with centre at 0 and radius…

Q: Rewrite the following integral using substitution: sẽ (1 + 3x)?dx

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Q: -4x dx | xe

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Q: yea-1) dxdy . /1+y²

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Q: Evaluate the following integrals: 1. tan? x dx

A: Given: I=∫tan2xdx We know that 1+tan2x=sec2x…

Q: Evaluate the following integrals: i. Se- cos(20)de ii. dx Va+100

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Q: Evaluate the following integrals by using the substitution u= 4x+ 1. %3D (a) 4x + 1) dx. (b) 4.x+1)2…

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Q: Evaluate the integral by making the given substitution. xV+ 14 dx + 14 dx, u = x3 + 14

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Q: S(In x)² dx

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Q: Evaluate. the. following.integrals..by.changing..the.arder. integrahian.s 2 405(x9 dxdydt a.…

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Q: Evaluate the following integral by reversing the order. 5a/2 1 || 3cosxdydx. "½ sinx

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Q: Evaluate the following integrals.

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Q: Evaluate the following integrals. (а) 1 (&r + 1)572 dx (b) -dx Vx

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Q: arctan(3r) da =

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Q: 1.4. S sin5xsin3xdx Ans:

A: Note: We shall answer the first question only as the exact one is not specified. Please resubmit the…

Q: Evaluate the following integrals.

A: To Determine: Evaluate the following integrals. Given: we have ∫tan7x sec4x dx Explanation: we have…

Q: dx (6-х?)3/2

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Q: e™ tan (eª) d.x J Vsec2 (e") – 7

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Q: Evaluate the following integrals: 4x (a) 3xet dx (b) / z In(2)dz (c) / 2°e d.x

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate the following integrals: e tan (e") (b) dr Vsec2 (e²) – 7

A: We have to find

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.