а. e-* dx 1 dx x + 1 b. 8.

Q: Evaluate the following integrals Sxcos(3x) dx 2. COS

A: topic - definite integral

Q: evaluate the given integral.

A: Then we use substitution

Q: 3 2—х ∞ Lo dx X¯e

A:

Q: Evaluate the following integral: dx So √1-x²

A:

Q: Evaluate the following integrals.

A:

Q: Evaluate the given integral. ∫ 5e-2x dx.

A:

Q: Determine the following integrals: ³ In r dx and

A:

Q: Evaluate the following integrals. (a) /; 1 dx - 4

A: As per bartleby expert policy, only first individual question is to be answered. Kindly repost the…

Q: y° cos(3y) dy

A:

Q: Evaluate the following Integrals dx しな25)メ

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Q: Evaluate the improper integrals: S xe-*dx (a) dx (b)

A:

Q: Evaluate the following integrals.

A:

Q: Evaluate the integral: Jo Sí(3xyY+ 5) dy dx Answer:

A:

Q: Find the following integral. x² In x dx

A: We find it integral by parts. Then:

Q: 23 dx 'e xyIn x

A:

Q: Evaluate the following integrals.

A:

Q: Evaluate the following integrals. 1. S(x² – 2)² dx

A:

Q: Evaluate the integral ? e1/x dx x2

A: we have to integrate by using substitute method

Q: Evaluate the following integrals: 1 = fx'e* dx 1. I

A: Given : Inetrgal equation is given

Q: Evaluate the given integral. 75 1 dy dx 25 + x 5.

A: We need to evaluate the following interval- ∫05∫x5125+x2dydx

Q: Evaluate the following integrals. a. dx Vx -1

A:

Q: 2 - dx x2 +1 01

A:

Q: 2 1 e dx e

A:

Q: dx 51. 1 + e*

A:

Q: Evaluate the given integral ∫ 2x/ e^5x dx

A: ∫2xe5x dx

Q: Evaluate the given integrals 1 (a)[ -dx 2 -

A: Given that: ∫1x29-x2dx

Q: Solve the following improper integrals DI d √x dx

A: Given improper integral  ∫0∞1xdx

Q: Evaluate the given integrals. 1. ſ cos v2x dx 2. fx a*dx

A: Please see the answer below.

Q: Evaluate the following integrals: 1) 3x(x-5) dx

A:

Q: Evaluate the following integrals: (3" – e") dx = -

A:

Q: evaluate the given integral.

A: To evaluate the given integral

Q: Evaluate the improper integral :S e dx

A: See the attached file for a step by step explanation to evaluate the given improper integral.

Q: Evaluate the following integrals.

A: Given integral is  Let us substitute  u=ex⇒du = exdx⇒dx=e-xdu ∫dxex1-e2x=∫duu21-u2

Q: (e) /a (с) dx e2x 2.х

A:

Q: 5. Evaluate the Integral ?(x²-2)"dx

A:

Q: (xe* dx

A:

Q: را Evaluat the following integral by reversing 2 e dx dy

A: It is known that ∫exdx=ex. The order of the integration can be changed by plotting the integration…

Q: Evaluate the following integral. 1 dx /x + 4

A: By using integration formula, we calculate the given integral.

Q: S xe2x*sin(e**)dx

A:

Q: i. L, Ix|e(1+x²) dx

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

Q: Evaluate the following integral. X'e dx

A:

Q: Evaluate the following integrals: (3 – e² ) da – e² ) dx =

A: To find:∫3x-exdx

Q: re3 dx De xyIn x

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: Evaluate the given integrals. 3x?dx 1. S 2х4—1

A: Given that a integration and we solve this problem by using general formula of integration.…

Q: Evaluate the following integrals.

A: Given:∫dxe2x+1

Q: b) Evaluate the integral x? e* dx.

A:

Q: Evaluate the following integrals 3 dx a) , -1 3x-2

A: ∫−103 dx3x−2Let t=3x−2dtdx=3⇒dt=3dxAs x=−1→t=−5As x=0→t=−2

Q: Evaluate the integral. 5 x2 e dx +C

A:

Q: evaluate the given integral.

A: To evaluate the integral: ∫ x2e-xdx Formula used: Integration by parts: ∫uvdx=u∫vdx-∫dudx·∫vdxdx

Q: Calculate the following integrals. dx (a)

A: Note:  As per our guidelines, we are supposed to answer only one question. Kindly repost other…

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.