x3 :/ V? +3 dt then If f(x) = 3 Evaluate the following definite integrals using the Fundamental Theorem of Calculus. s |81 – s2| ds = 485 81x2 sin(/x) dx 0. 18 t – 9 dt = t2 – 18t + 82

Q: Find the following definite integrals. (a) Sx³V2+x² dx (b) Sx² In x dx (c) S3e-2* sin x dx

A: Use Integration by parts and substitutions method

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integrals. 3 (x + 1)² dx…

A: See the details solution in the details

Q: Evaluate the following definite integrals.  1. ∫04 (3x - (x2 / 4)) dx 2. ∫-11 ((√3x)-2) dx 3.…

A: Q 1. Consider the definite integrals: ∫043x-x24dx To solve the given integrals: ∫043x-x24dx=∫043x…

Q: Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral. a) S(1 + 3x –…

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

Q: 2. Find the following indefinite integrals. 1 dx (a) 16 – [In(x)]² 1 xp (b) | x?+ 2x + 26 / A 1 (c)…

A:

Q: Find the indefinite integral. | t17 dt : +C

A:

Q: 2. Evaluate the following definite integrals: S dx -22-x b. S32 sinx dx а. С.

A:

Q: Find the indefinite integral of the following function. ncos(6 )dt sin(6t) 6 O cos(6 m) +C 6 sin(6…

A: i) ∫πcos(6 πt)dtii) ∫253u du

Q: 11. Evaluate the following integrals. sinx dx 1- cosx dt fxsec' x dr b) a) c) t2 +81

A:

Q: Find the indefinite integral. (8ti + j + k) dt + C

A:

Q: Evaluate the indefinite integral. 2 (t) – 7e' + 8 + 1 + 12 2 sin(t) – 8 cos(t) + sec- dt = +C.

A:

Q: Calculate the following definite integral: |x² – 1| dx -2

A:

Q: Evaluate the definite integral. cln 8 So° f (x) dx, ƒ (xæ) =6e* /(5+e*)

A:

Q: Evaluate the following Integral by using suitable method: 2y3 +y y4 + y² + 1' ª |7 +e-4y . -) dy

A:

Q: Compute the indefinite integral of the following function. r(t) = (4 sin t,3 cos 8t,7 sin 6t)

A:

Q: 10. Evaluate the definite integrals by u-substitution. In5 Te(3-4e) de ( 2 cos 3x dx b. а.

A: a. ∫0π62 cos3x dxb. ∫0ln 5ex3-4ex dx

Q: Calculate the following definite integrals. -1/2 1 dx "dx dt (t+2)³

A: As per the company guidelines we can solve first three parts. I hope that the given solution will…

Q: Find the indefinite integral. t2 dt 3= t3 +C

A:

Q: 2 Evaluate the definite integral 16sin(t)cos (t) dt.

A:

Q: Evaluate the following indefinite integrals: a) ∫ (1/x + 3/x2 - 4/x3 ) dx b) ∫ (x2 + 2x - 5) / √x dx…

A: The derivative of the function is the measure of how fast the function is changing with respect to…

Q: Evaluate the following definite integrals: i. ∫0  -1  (xe^(-x2+2)) dx  ii.∫1   0  (x^4+7e^x− 3) dx

A: To Evaluate the following definite integrals

Q: Consider the following. 0.4 x2 xp V4 - 25x2 4 – Let x 2 sin(0) and determine the following. dx = de…

A:

Q: Find the following indefinite integrals if a, b and c are positive real numbers, with a +-1 and b +…

A: Note that a≠-1 and b≠ 1    then we can solve these integral

Q: Find the indefinite integral.

A: we have to evaluate the value of the given indefinite integral: ∫t2-3-t3+9t+1dt let the given…

Q: Evaluate the following real integrals by residue theorem 3 03 S <-1 X Sin mx X4 +1 OSH dx πT -m/√z…

A: As per the question we are given an improper integral from -∞ to +∞ and we have to evaluate it by…

Q: Find the indefinite integral. ∫(e1t/t2) dt

A: Given: I=∫e1tt2dt for evaluating given integral, in given integral we substitute  1t=p…

Q: 4. Evaluate the following definite integrals using the Fundamental Theorem of Calculus and…

A: (a) ∫-22 (3x2+5x-4)  dx∵∫(3x2+5x-4)  dx = x3+52x2-4xSO,∫-22 d x3+52x2-4xby fundamental theorem of…

Q: Find the indefinite integral. S(e¹ i + j + costk) dt O e¹i + tj - sint k O e¹i - sint k O e¹i + tj +…

A:

Q: Q1) A-Evaluate the following integrals: 1) S (cos x/ sin? x) dx. 2) S (2x+4)1/3 dx, use x-0 to x=2.…

A: We have to evaluate the given integration.

Q: Evaluate the following indefinite integral: 2(1 + e*) dx (x + e*)3

A:

Q: (a) Evaluate the following integrals: π cos(x) dx dy 4y

A:

Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: 5 (a) [√4x In (V√x)] idx…

A:

Q: Find the indefinite integral ∫ t/√(1 − t4) dt

A: Given integral, ∫t1-t4 dt

Q: Find the indefinite integral of t/1+t

A: Here we have to find the indefinite integral of t/(1+t) .

Q: Find the following indefinite integrals subject to the initial conditions 2572 b) y"= (x + 1)/2 with…

A:

Q: Evaluate the definite integral. 2 St³√₁+t² dt 0

A:

Q: 3) Evaluate the following definite integral : 8 x V 1 + x dx I

A:

Q: 9. Determine the following antiderivatives: | sec?(x) tan(x) 4x (2x² + 3)° dx а. b. sin(2x) -dx-…

A:

Q: 8. Evaluate the definite integral. (a) "(1+ sin x) dx =2+7 xP z/ Z- e (b) хе

A:

Q: 2. Calculate the following transcendental integrals: a) S² exee* dx X b) S (x²+1)In (x²+1) dx cos…

A:

Q: i +j- t3/2 k ) dt |

A:

Q: 64 1 (c) Ltd (√t - 1 - / t + √²) de dt √t (d) * (sin(2x) + cos(2x)) da 0

A: To evaluate the following definite integrals using the Fundamental Theorem of Calculus.c ∫164t-1t+t3…

Q: Evaluate the definite integral. *2 e 1/x* dx J1 +s

A:

Q: Evaluate the following definite integrals. (a) | |2t – 4| dt. T/6 (b) cos(3x) dx. e (c) dx.

A:

Q: 1 4 dx 2 /1 – x²

A:

Q: Evaluate the following definite integrals. (а) |2t – 4| dt. /- (b) cos(3x) dx. (c) d.x.

A: You must have an idea about definite integral to solve these questions. In these types of integral…

Q: Evaluate the following definite integrals using the Fundamental Theorem of Calculus. s 49 – s2 ds =…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Evaluate the following indefinite integrals. xª + 6x² )1 ا( o - x +4 1 a) / * sin(®)dr r3 + 4x |

A:

Q: 1. Evaluate the following integrals: g) . dx sin-1 x V1 – x2

A: Since you have posted more than one question we solve the first one for you. For the remaining…