Consider the indefinite integral 9e9x dx: (e9r + 2)® This can be transformed into a basic integral by letting 9x + 2 o and U = du V o dx Performing the substitution yields the integral 1 X du Integrating yields the result 1 +C 5 (e9x + 2)

Q: Evaluate using integration by parts. .6 In (x)dx 6 In (x)dx =| 1 (Type an exact answer.)

A:

Q: ind the double integral of x(ey) [0,1] x [0,1]. Explain why either A(x)dx or A(y)dy is easier to…

A: Calculate the double integral:  ∫y=01∫x=01xeydxdy=∫y=01eydy∫x=01xdx…

Q: Suppose we make the substitution u=6+x in the indefinite integral - dx What is the 6+ x4 resulting…

A:

Q: -Find the Integration of by Simpson's rule knowing that: Fex) - dx > Use 1.0 1.5 3.0 72.0 2.5 4.0…

A: Given that a=1.6, b=2.8, n=4 x 1.0 1.5 2.5 3.0 4.0 fx 0 8.625 43.875 72.0 153 Now, Simpson's…

Q: a a²-x² xe?y q2 dy dx Consider given double integral above and give answers to following two…

A:

Q: x³ + 6x² + x +2 fx-1 ax + In{(x + 1)*(x² – x + 1)| +- 2 Tan Ve The resulting integral of -1 + C,…

A:

Q: 9e9z Consider the indefinite integral dx: (e9z + 2)° This can be transformed into a basic integral…

A: To evaluate the integration.

Q: The value of the improper integral 42 x² e¯¤* dx 1 - 14e 14e-1 - O 14e-1 O 42e-1 O – 42e-1

A: Explanation of the solution is given below...

Q: (6x³ + 3x? x² – 16 89x – 52 dx Consider the indefinite integral Then the integrand decomposes into…

A:

Q: Evaluate the improper integral if it exists e'dx: 00 1 -1 0 e.2 O -e 3 O The improper integral…

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

Q: Consider how we can evaluate this integral using u-substitution: - dx. (3z+1)ª If we let u = 3x + 1,…

A:

Q: Given dy – sin(x))dx + cos(x)dy, where C is the triangle with vertices (0, 0), (1/2, 0), and (t/2,…

A:

Q: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

A: We can rewrite the given integral by using this substitution u = x1/2

Q: Evaluating the integral | (2x +e -)dx gives: 4 +e* – 2 ln x +c O A. 4x² +e* – 2 In|x|+c O B. x* +e*…

A:

Q: 00 1 Evaluate the improper integral 1 dy dx as an iterated integral. x³y 2 e-X The value is

A: We apply first integration on y then on x

Q: Consider the following. Let u = 4x³ - 1. Find du. du = dx Indicate how the limits of integration…

A: The given definite integral,          ∫01x24x3-14dx

Q: ( a ..    )Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2…

A: Given, ∫01cos2x dx

Q: Q2/Evaluate the integral: -1.57 9-x2 dy dx by changing the order of integration.

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

Q: 4 Evaluate the follwoing integrals. Show your work and state any appropriate methods you use. (a) 10…

A:

Q: Find the most general antiderivative (a) Integral [ (cos(ln x)) / x ] dx (b) Integral [ (x2)(ex^3)…

A: Given (a) ∫coslnxxdx  (b) ∫x2ex3dx  We have to find the most general antiderivative.

Q: 2e Consider the indefinite integral dx: (e2z + 3)* This can be transformed into a basic integral by…

A: Given,

Q: Evaluate the iterated integral. 40 (xªy-7xy) dy dx 0-4 40 jjov (xªy-7xy) dy dx = [ 0 - 4 (Type an…

A: The given integral,    ∫04∫-40x4y-7xydy dx

Q: Consider the indefinite integral dz: (e-2= + 2)5 This can be transformed into a basic integral by…

A: We have to solve the integration

Q: 11. The integral of an(In|4x=12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. С. 4 D. I

A:

Q: Consider how we can evaluate this integral using u-substitution: x S dx. √2x+1 If we let u = 2x+1,…

A: This question can be solved by integration by substitution.

Q: 2. Evaluate the indefinite integrals. (a) fx² - 2e*dx (b) Evaluate (3-4x)¹5 dx

A: We have to evaluate the indefinite integral

Q: y= cos 3x, for 0sxsn a. Which of the following is a simplified form of the integral? 元 OA. -3 cos 3x…

A: Formula Used: length of arc:

Q: The value of the improper integral |6 a e" da = 6 x e dx = 1 O 6e-1 бе 2e-1 – 6e 6e-1 - - 2e-1 -

A:

Q: Q2/Evaluate the integral: 1.57 9-x2 dy dx x, by changing the order of integration.

A: The integration order can be changed by changing the inner integral to outer and outer integral to…

Q: Evaluale the integral (i+2) sinz 23 dr. dz, where C: 12) =1, by any two methods and compare the…

A:

Q: Evaluate the double integral. eln 3 3 7 dx dy In x ey In 3 3 7 dx dy = (Type an exact answer in…

A:

Q: 39.: * Compute the integral: x (Inx) dx. a. (5e –1) b. (3e -1) c. (e +2) d. (5e -e') (e* -e) 32 16…

A: Use by parts integration

Q: Evaluate the improper integral if it exists e'dx: -0- e .2 O -e.3 O The improper integral diverges 4…

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

Q: Find the indefinite integral. x² + 4x + 1 - 6x² + 3x + 6 dx Step 1 du/dx dx = - du Let u = Begin by…

A: Given- ∫x2+4x+1x3+6x2+3x+6dx Solution-        Let u=x3+6x2+3x+6 Now, differentiate the above…

Q: (2x +)x dx | (28 + 4x5 + 4x²)? sing u-substitution and transformation of the integrand, then the p…

A: We will solve the integration using substitution.

Q: A few difficult integrals: (a) 1+ Vx (b) jV4 -x²dx (c) fx'e* dx try a substitution x = 2 sinu…

A:

Q: Evaluate the integrals: 1- dx TT/2 7cos t sin t dt 0. 2-

A:

Q: 6x Evaluate the indefinite integral. 6e sin (e) dæ U = du 9e9x dx %3D Substitution gives du…

A: u=e^(6x) is the right substitution for this problem

Q: Evaluate the integral. dx 7 X> 4 V16x? - 49 Which substitution transforms the given integral into…

A:

Q: السؤال 8 Evaluate the improper integral if it exists e'dx: - 00 -e.1 O e.2 O .3 0 The improper…

A: We will evaluate the integral and check if it converges.

Q: Evaluate the improper integral if it exists e dx: -00 The improper integral diverges 1 0 e.2 0 -e .3…

A: The solution is given as

Q: Evaluate the integral. dx (х — 4)(х — 8) (Use symbolic notation and fractions where needed. Use C…

A:

Q: (a) Solve the following integrals. (i) (ii) x' + 3x? – 10 - dx x(x – 3)(x+1) Integrate er* cos (3x)…

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

Q: 3 Given that / et dx = e3 - e, use the properties of integrals and this result to evaluate (4ex - 5)…

A: To find the integral by using the given results.

Q: One of the following is an improper integral. cln 3 e* dx dx J, xV16 – In x In 2 V4 - ex In 2 CA dx…

A:

Q: 8x dx Evaluate the given integral: J 1x2-5

A: Recall: ∫1ax+bdx=1alnax+b +C; where 'C' is an integration constant.

Q: Calculate the definite integral. 4xy Vx2 + y2 dy Calculate the iterated integral. (1 (1

A: Here we have to calculate ∫014xyx2+y2dy

Q: (a) Find the approximations T10 and M10 for ∫12 e1/x dx.(b) Estimate the errors in the…

A: (a) The interval of integration is 1, 2 and we need 10 equal subintervals, so, we need…

Q: 23. (a) (2n )! [P,(x)]² dx 2 (n!)ª J_, (1 – x*y" dx (b) By making an appropriate change of variable,…

A:

Q: Consider the indefinite integral (5x³ + 4x? 73x – 52 dx 16 Then the integrand decomposes into the…

A: