13. b n b-a Use the equation f(x)dx lim fa+k- to evaluate the following definite integral. n n-oo k 1 a 0 (9x-2x2) dx -3 0 (9x-2x2) dx (Type an integer or a simplified fraction.) -3

Q: 12. What value of b> - 1 maximizes the integral? b A nolh | x-(1-x)dx Simplify-1 following…

A:

Q: 1. Evaluate definite integral. [(2 - y)-y]dy 0.

A: Consider the given integral: ∫042-y-y2dy

Q: Q.1 Find the integral of f 2 /x+ e* ) dx. - 3

A: We will find the integral as following.

Q: 10) Suppose that f is continuous and that f(z) dz = 0 and f(z) dz = 5. Find - 6f(x) dx . -3 -3 A) 30…

A: ∫-33f(z) dz = 0  ,    ∫-35 f(z) dz   = 5find -∫356f(x) dx∫abf(x) dx    = ∫acf(x) dx   +∫cb f(x)…

Q: 1 So x2-4 dx an improper integral. (5 points each) 3. Find a value of b >0 that makes

A: Given the function :

Q: 5 Find the following indefinite integrals. 10 a. f(x+2)' dx b. J d. [4 (3-&x) dx c. (3x-7) xp-

A: c)

Q: (2+금) 3 29 7. Suppose that lim In Fill in the boxes for the corresponding equation -- - - '(2+금)% n…

A:

Q: 1. Find the definite integrals of the following functions : (a) L. 4.x dx (h) dx ex +1 -2 0. (b) /…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: "(2) – 16f(2)) sinh(4x) dr Find the value of in terms of f(0) if f(a) = f'(a) = 0. %3D f(0) O f(0)…

A: See the calculation below  Fourth option is correct

Q: 3 [²(x²) dx 0 Using the definition of definite integral, ff(x)dx= lim f(x) Ax, and the given…

A: Given, ∫03x2dx

Q: 3x -dx x4 + 1 Evaluate the indefinite integral. + C

A:

Q: 11. Rules of Definite Integrals: If f(x)dx = 12, S." f(x)dx = 6, and "f(x)dx = 4, find the…

A: Given that: ∫05f(x) dx=12∫512f(x) dx=6∫812f(x) dx=4

Q: ₁√x³ √4-x² dx. if we let z = √√4-x², which of the following integrals is correct using rationalizing…

A: The given integral,        ∫x34-x2dx

Q: 16 -3t – 3 What is the value of the definite integral dt? Enter your answer as an exact fraction if…

A:

Q: 13. Consider the integral | - dx then (which statement(s) is/are correct): x2 - 4x (i) dx : x - 4x…

A:

Q: 2. 1 Evaluate the definite integrals below. Use u-substitution when appropriate. 4 5 3el/x (a) (b) |…

A:

Q: 12 1 3. Find the exact value of the definite integral | dx (x+6) Vx- 3

A: The given definite integral can be evaluated using the method of substitution by making the…

Q: Q1 (a) Integrate the following definite integrals using suitable method: (i) S, tan-1 x dx (ii) a dx…

A: To evaluate the given integral

Q: B. Evaluate the following integrals: x-9 1) S- dx x2+3x-10

A:

Q: ∫(−6x6−2x3−4)dx

A:

Q: 4. If the integral value of | f (x)dx = 4 and | f(x)dx =-3 then the value of | f(x)dx is -1 -2 а. —3…

A: It is given that  ∫-14fxdx=4∫-24fxdx=-3

Q: 13)Evaluate 13 Evaluate the integral s 5x--Xt27 dx x (x²+G) -1 3 tan 3+C b)(-ト2フx)、1mlxCx?ss)1c Sx3…

A:

Q: 9 Evaluate the integral f 2x (x² + 1)° dx using the substitution = x² + 1. и — с 2.x (x? + 1)° dx +C

A:

Q: 1. Evaluate the integral of x2 (3 - 2x) dx if upper limit = 2 and lower limit = -1. а. 12 b. -12 C.…

A:

Q: 9-x2 18-x²-y² xydzdydx. B: Find the integral fo J

A: Triple integral

Q: 2 Evaluate the definite integral S: 1 dx. 1 x+a2 ter -17 a- 19

A: solution:

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

A: Given,

Q: Evaluate the definite integrals using the graph of f (x) below. 4- 2- 10 12 -2- -4- -6-

A:

Q: Solve the Indefinite Integral. xe²t S dx (2x+1)² A [1-21] +0 e2x 2x C 4 2x+1 B. 2-2(22+1) + C 4 C.…

A: SOLUTION-

Q: (9) Evaluate the indefinite integral f X+2 dx x² + 4x 2

A:

Q: 3 3 Use the values f(x) dx = 5 and g(x) dx = 2 to evaluate the definite integral. (a) | 39(x) dx (b)…

A: Given query is find the values of given integrals.

Q: 13x? + 17 What is the indefinite integral of ) dx (2x+1)(x² + 4

A:

Q: 4.1 Given ∫(−2x6+3x5−3x3−6)dx, evaluate the indefinite integral. Do not include +C in your answer.

A:

Q: 5. S,(x-4)(x2-8x – 1)3

A: Solving the given integral.

Q: 3. Evaluate the definite integral. Give exact answers S(x² + 2x – 4)dx - a. ~2 2x+1 dx Vx2+x-2 b.

A: Take integration. Follow step 2nd .

Q: 8. Find the value of the constant C for which the integral 11x 11C dx x* + 1 4x + 1 converges. C =…

A:

Q: Find the value of the following definite integrals. Show your solution. 1. f(x¹+4) dx 2. (cos x +…

A:

Q: 1.0) Find the following indefinite integrals: 1.1) ∫ (5 + x7) (3x2 + x-4) dx

A:

Q: The following integral is  The integral of g(x)dx from 7 to 2

A: The given integrals are,

Q: Q-3: Find the general indefinite integrals of: cos ntcos(sin(nt)) dt 2. Vx2 + 2x dx

A:

Q: Can i get help step by step with this problem?

A: Given,

Q: Evaluate the integral. dx (х — 13)(х — 23) (Use symbolic notation and fractions where needed. Use C…

A: Explained below

Q: 7. (4ea) Evaluate the definite integrals. a) L (3x2 + e*) dx

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

Q: 1. Use properties of the definite integral to solve the following problem. f (x)dx = -3 and f(x)dx =…

A:

Q: 2) evaluate the indefinite integral £x² 9+X² dx

A: The main objective is to evaluate the integral. The integral formula is ∫xndx=xn+1n+1+C, where C is…

Q: 4. Suppose f(x)dx = 2, f(x)dx= -5, and g(x)dx--5. Evaluate the following integrals, 2. g(x)dx = 7.…

A:

Q: 3. (а) Evaluate the indefinite integral 2Varctan(3x) dx. 1+ 9x² •16 (Б) Suppose we know that (3f (x)…

A: (a) We need to evaluate the following integral ∫2arctan(3x)1+9x2dx (b) We need to evaluate the value…

Q: 1/2 2. Evaluate ( x*(1– 2x)°dx

A: Given: ∫012x41-2x3dx

Q: 7 Suppose f(x)dx = - 3, f(x)dx = - 6, and g(x)dx = 3. Evaluate the following integrals. 2 2 2 g(x)dx…

A:

Q: 1. Use algebraic manipulation and (if necessary) u-substitu- tion to integrate the function. (a) /…

A: Hey, since there are multiple questions posted, we will answer the first three subparts of the…