The indefinite integral of (1,2r, e') is (a) (0,2,e')+C. (b) (1,",e') + C. (c) (r+C,r' +C,e' +C). (a) O (b) O (c)

Q: Find the general indefinite integrals integral of x(x3+2)2dx integral of 3x2(x3+1)4dx

A: The given integral of  xx3+22dx     =    ∫xx3+22dx = ∫xx32+2(x3).2+22dx  = ∫x7+4x4+4xdx =…

Q: / 1 – x2 dx (c)

A: Given I = ∫1-x2x3dx    ......... (1) Integration by parts ∫u(x).v(x)dx = u(x)∫v(x)dx…

Q: Find Lebesque integral of function on segment (-3,0) 1 f(x) = %3D x+3

A: Given, fx=1x+35 Let, A be the set of all rational number in -3,0. Here, mA denotes the Lebesgue of…

Q: calculate the indefinite integral.

A:

Q: What should be the rewrite of the integrand of (2x + 5)² dx so that the resulting integral is…

A: Topic = Integration

Q: Evaluate the integrals using integration by parts. ∫x sec2 x dx

A:

Q: Evaluate the indefinite integral using u-sub. Show all work. 2x+4 dx

A:

Q: Evaluate the integral using formula was (from the 1page differentiation & integration formula) by…

A: Hint : 1. Use substitution : ex = t. This integral will turn into a standard Integral.

Q: com Ise Find the indefinite integral using integration by pa x cos 9x dx;u= x, dv = cos 9x dx egin!

A:

Q: Show that arctan(Tx) – arctan(x) -dx In T. by first expressing the integral as an iterated integral.

A: To show

Q: Compute the double integral (either in the order of integration given or with the order reversed).…

A: Given: ∫01∫arcsinyπ21+cos2xcosxdxdy

Q: Use Property 8 to estimate the value of the integral.

A:

Q: Can we evaluate the integral of 1/(x^2+2x)^3/2 dx by using x= sec¿ - 1

A: Consider the equation

Q: Evaluate the indefinite integral Fl the substitution rule 2x+3 dx Vx+3x+ 5

A: Topic: integration

Q: Determine the following indefinite integral. Check your work by differentiation.

A: The given integral is Simplify the integral

Q: What change of variables is suggested by an integral containing V100 – x??

A: 100-x2

Q: Determine the following indefinite integral. Check your work by differentiation.

A:

Q: Simplify down to a single integral in terms of . .3 /9-x² 63–42²–4z² Volume = 1 dy dz dx = Σ da.…

A: ∫-33∫-9-x29-x2y3x2+3z263-4x2-4z2dzdx

Q: nich integral represents the length of the graph of y = In(1 – x²) over the interval [0, ]:

A: here option A is true because length is given by =1+(dydx)2dx so here…

Q: Use IBP to evaluate the indefinite integrals. 1. ∫ x³sin x dx 2. ∫ sec³ x dx 3. ∫ x cot² x dx

A:

Q: Use integration by parts to prove the reductionformula.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: integral

A:

Q: integral

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

Q: There is a line through the origin that divides the region bounded by parabola y=x-x^2 into two…

A: Given There is a line through the origin that divides the region bounded by parabola y=x-x^2 into…

Q: Why does Hm have minus x in front of it. How did they do integral?

A: Both the questions are explained in step 2.

Q: Find the indefinit integral of (3-2x)2 dx

A: Given ∫3-2x2 dx

Q: Find indefinite integral.

A: ∫5lnz+3z dz Put, 5lnz+3=t⇒5·1z+0=dtdz⇒1zdz=dt5

Q: indefinite integral of (7 + ex) dx

A: Consider the given indefinite integral:

Q: In x dx 5.

A: Our Aim is to ∫ln (x)xdx -(i)

Q: Calculate the indefinite integral S (2Vx3+3)(2Vx3 – 3) dx

A:

Q: Express f, 4xyz dV , where E = [0,1] × [0,2] × [0,3] by using different orders of integration. Hence…

A: To find the value of the integral

Q: Evaluate the integral using integration by parts where possible. x In(8x)dx

A: Given: ∫12 x ln(8x) dx To find: Value of the integral.

Q: (c) in the tank to a height of 1 m above its top. Give a definite integral that computes the total…

A: answer is in next step

Q: Evaluate the integral of cosh2x(sinh 2x)^2 dx

A: ∫cosh2xsinh2x2dx

Q: 4. Calculate the indefinite integrals for the following functions as integrands (section 8.3): 1 (a)…

A: Recall: ∫x2-a2 dx=12xx2-a2-12a2logx+x2-a2+C

Q: et dz V1-e2x

A: Given problem:-

Q: an

A:

Q: Calculate the integral approximations Ts and Ms for L'(In x)-2 dx. Your answers must be accurate to…

A:

Q: compute the integral of    "(sinx * tanhx ) / ln(x+0.01)" from 1 to 5 to at least 6 significant…

A: Given :  ∫15sinxtanhxlog(x+0.01)dx

Q: Provide an example of an indefinite integral that when integrating requires r as a substitution. As…

A:

Q: Use Property 8 of integrals to estimate the value of the integral. ∫20(x3-3x+3)dx.

A:

Q: dx V1-x -1

A:

Q: the indefinite Integral In(cosh x + ex)- A In(cosh x +ex) Sinh x + e* cosh x + ex (В sinh xtex sinh…

A:

Q: 10. f3, (x²-1) dx

A:

Q: sds 3. V3s² +1

A: Given: ∫sds3s2+1 Let u=3s2+1, duds=6s Then ds=16sdu

Q: Use integration by parts to evaluate the integral. | (In(3x))*dæ- 8, +C

A: The given integral is ∫(ln(3x))2dx. Let  3x=u. Differentiate both sides.    3dx=du⇒dx=13du…

Q: Compute integral x^2cos(x^3+3) dx

A: Given : ∫x2cosx3 + 3dx