,3 dx (x2+а2)3

Q: What is the integral of (3t – 1)³ dt?

A:

Q: 3 dx 2 х2+1

A: Given problem:-

Q: Find value of a&b without using integration by part

A: Given     To evaluate   a and b

Q: dx V1+x² 19

A: Given:∫x51+x2dxlet u=x2+1x2=u-1x4=(u-1)2 dudx=2xdx=12xdux4=(u-1)2 substitute above in the…

Q: Using Laplace transform find the solution of the differential equation +4xe -2 with x(0) = 0 and…

A: The given differential equation is  d2xdt2+ 5dxdt + 4x = e-2t x(0) = 0,     x'(0) = 1

Q: Use integration to find a general solution of the differential equation. (Use C for the constant of…

A: In order to determine the value of y, the given function needs to be integrated by substitution.

Q: Solve the nonhomogeneous differential equation given below. Your answer should contain two…

A:

Q: 12. [-/5 Points] DETAILS HARMATHAP12 13.2.051. In this problem, use properties of definite…

A: Given below the detailed solution

Q: In electromagnetic theory, the magnetic potential uu at a point on the axis of a circular coil is…

A:

Q: 2y" + 3y' +y = +3 sint

A: To find the solution of given differential equation  by using the undetermined coefficient method…

Q: Suppose that a dimension X in the area A= 6x*2 of a shape are differential equations functions of t.…

A: Here we differentiate the function with respect to ' t '

Q: Solve the integral. x5 + 3 1. х?(x2 + 2х + 1)

A: Given that  The integral  Using the partial fraction decomposition find the value of the integral

Q: Integral Calculus: Integration by parts

A: It is given that the integration ∫ydyy-14. Note that  The integration by parts formula  ∫udv=uv-∫vdu…

Q: In 2 e2x dx /1 + e*

A: power rule: ∫undu=un+1n+1 Use basic rules of integration to solve the problem.

Q: -x e 4e dx

A: Given: I=∫e-x33-x4e-xdx

Q: S (sin'x-sinx-x' sin* x+x²sin x) dx ? :-x° sin* x + x² sin x) dx ? What is the value of the…

A:

Q: dx V2 – 5x2

A: We have to find

Q: ion 8 apply General Power Formula of Integration on which of the following sinhucothudu cosha coshu…

A: We have to choose the correct option from the given options

Q: Find differential equations that refer to nomogeneous or discrebe Ezscu transforinations Jeneral…

A: To find: The general solution the given differential equation. Given information: The differential…

Q: x-1 dx (x+1)5(x-3)5

A:

Q: 6. f In² x dx

A:

Q: 3. Vsin x+1 cos.xdx

A: Solution

Q: Solve using 2 methods: a.) Laplace Transform b.) Ordinary Differential Equation

A:

Q: reduction formula to evaluate the integral. x e 4Xdx

A:

Q: 30. Someone is doing implicit integration and has reached this point. Please do the next step (only…

A: The objective is to simplify the given expression

Q: identify the integration technique or formula to guide in obtaining the particular solution of the…

A:

Q: e cosx sin x dx 1-e2 cosx

A: Given problem:-

Q: Romberg Integration - example dx=2 compute R5,5 Sinx dr

A:

Q: t' sin(2t*) dt

A: given,       ∫t7sin2t4dt

Q: tan ydy (1+ln(cosy))3/2

A:

Q: х3 dx (а2-х?)2

A: Given integral is ∫x3dxa2-x22

Q: Solve the integral. dx 6. 1 – 4e2x

A: We need to solve ∫dx1-4e2x Let u=2x Differentiate both sides with respect to x. dudx=2⇒du2=dx…

Q: | (423 – 92² + 7x + 3) e¯² dæ

A:

Q: Integrate xcos (2x² + 7) d×

A:

Q: x* – /x dx бу 4

A: integration

Q: Log integrals Use integration by parts to show that for m + -1, f )+c x" Inx dx In x - т +1 m + 1…

A: Given: verify that ∫xmlnxdx=xm+1m+1lnx-1m+1+c, ∫lnxxdx=lnx22+c for evaluating first integral we use…

Q: Sy cos y· sin²y dy

A: Given: I=∫y.cosy.sin2ydy

Q: 6x² +- dx S(cos(x)+ sec*(x) dx

A: SOLUTION-

Q: Solve the integral equation y =2+

A: Here we use Leibniz Rule .

Q: Сompute 1. f dx, where f(x)=|x|.

A:

Q: -3 -t Evaluate the integral: Soft²eu du dt е

A:

Q: dy 1.5: ey sin( e-y)

A: To evaluate the given integral: I=∫dyeysin(e-y)

Q: S sec20 · tano(1+ 3tane)ž do

A: To determine the indefinite integral.

Q: (§5.3, Q34) Evaluate the indefinite integral. Remember, there are no Product, Quotient, or Chain…

A:

Q: Use integration to find the general solution to the differential equation. (Use C for the constant…

A:

Q: 1 х-х2 dx -8 2

A:

Q: I. INTEGRATION BY. PARTS; 2.).) xsin 9x COs 4x dx - xcas (4x) + (x +s ANS = X COS * sin (8x)) + C

A:

Q: give 3 examples of constant rule of integration formula give 3 examples of power rule of…

A:

Q: Solve the differential equation. (Use C for the constant of integration.) 4x2 dy dx V2 + x .3 %3D

A: See below the answer and calculation

Q: Use integration to find the general solution to the differential equation. (Use C for the constant…

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.