show the steps of this integral: | dxp In p = In a H

Q: Evaluate each integral bY first making an a substitution. appropriate Sx(x²-1)" dx ल मैंढ a)

A: .

Q: Evaluate the integral. | x sec (4x) dæ =| +C

A:

Q: rp= dx bo 1. to

A:

Q: Evaluate the integral / -2(In x)? dx

A: Given,         ∫-2lnx2dx

Q: A? : da dy 2π

A:

Q: EN

A:

Q: Find the integral +1 dr = +C

A:

Q: Evaluate the integrals in Exercises using integration by parts

A: Solution of the given integrations can be found with the help of the integration formulas and…

Q: a) Calculate the integral , dzdy dx.

A: Given:

Q: | Vx+ + x6 dx

A: Given: The integral expression as ∫x4+x6dx, To evaluate: The value of given integral.

Q: 2 t + 13) dx

A:

Q: Compute this integral ∫( sqrt((e^x) +1) dx

A: To Compute this integral ∫( sqrt((e^x) +1) dx

Q: Calculate the following integral if a=3 and b=7. t3 - 13/2 dt Give your answer correct to 2 decimal…

A: Given: The following integral: ∫abt3-t32t4dt, a=3 and b=7.

Q: Find a formula for the function represented by the integral 3t dt

A: Please refer to the image below.

Q: -2x d.x. | (a² + 1)e .2

A:

Q: Find the answer to this integral:

A:

Q: [(b) find the integral in the interval [1,4] S(3/2 sqrt(x)-4/x^2) dx ].

A: To evaluate the given integral on [1,4]

Q: Evaluate the integral by making the given substitution. sec(2x)tan(2x) dx, 2x +C

A: Solving the problem by doing the integration.

Q: Express the integral in terms of the variable u, but do not evaluat e21 In x dx; u = In x re21 In x…

A: We are asked to evaluate the integral.

Q: Evaluate the integral.

A:

Q: Efxe*dx (1+x)2

A:

Q: Evaluate the integral in terms of the constants.

A:

Q: 1 -dt , find g'(2). V4 +t5 If g(x) =

A: Let's find.

Q: dt (2 – t4)4

A: Given, ∫-10t3(2-t4)4dt

Q: 3x 2 dx

A:

Q: Evaluate the integral. In(10 x 9) dx +C

A:

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: 3 dx

A:

Q: VIt VI dx тр. a.

A: According to our policy at Bartleby, I can solve only one question. Given an integral : I=∫1+xx dx…

Q: Evaluate the integral.

A: The given integral is ∫1+ex2exdx.

Q: Evaluate the integral: 5x sec (x) dx +C

A: Recall: ∫u.v dx = u∫v dx -∫dudx∫v dxdx   ( Product rule of integration) ∫ sec2x dx = tan(x)+C…

Q: Find the integral by using the integral table on the inside bac dx x(x + 5) + C

A:

Q: Evaluate the integral.

A: Given; ∫011+e-xexdx Integral the above expression  ∫011+e-xexdx    Let 1+e-x=t Differentiate with…

Q: Evaluate the integral by interpreting it in terms o 0. 9 - x2 ) dx -3 9 3 + 4

A: ∫-30 (3+9-x2)dx=∫-30 3dx+∫-30 9-x2dx                                    =A+BA:∫-30 3dx=3x|-30…

Q: Find the value of the integral. n dx. 2

A: Given,          ∫-π2π2π dx

Q: Evaluate the integral. | In(7 x – 6) dx = +C

A: Given query is to find value of the integral.

Q: Find the integral by using the integral table on the inside back cover. (Rer 25x2 +36 dx + C

A: We will use substitution

Q: evaluate the integral 17/((x-1)(x^2+16)) dx?

A: Evaluate the integral .we use partial fraction method to solve this integration. Here i attached…

Q: Sx²e=* dx Sx²e¬

A:

Q: Evaluate the integral Se*dx

A: We can solve this as follows:

Q: Evaluate the integral by making the given substitution. dx (3x + 14)4 u = 3x + 14

A: We have to solve

Q: 4. 1) ŝ dy

A: The given integral is, ∫y7y4-113dy The objective is to solve the integral by substitution method.

Q: çin fxa-lex®dx dx 3?

A:

Q: Find the integral 1 dx = 9 – x²

A: We have to find the integral: ∫0119-x2dx Simplifying the question so that we can use the table of…

Q: problem in photo attached

A: The question is in the form of functions involving exponential function

Q: 3. t dx

A:

Q: Evaluate the integral 1 dx

A:

Q: evaluate the integral or state that it diverges.

A:

Q: | VI (2 – x)² dx

A: Given ∫18 x3(2-x)2 dx                            ⇒∫18 x3(4-2x+x2) dx⇒∫18 x13(4-4x+x2) dx⇒∫18…

Q: Evaluate the integral or state that it is "divergent 1 dx х?(х — 1)

A: To evaluate: ∫1∞1x2(x+1)dx Use partial fraction decomposition to simplify: 1x2(x+1) Let,…

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.