Evaluate the following definite integrals using the Fundamental Theorem of Calculus. s 49 – s2 ds = -14 sin(Vx dx 49т 2 14 t – 7 dt = t² – 14t + 50 II

Q: 5 a Væ – 4 dx ,2 J4

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

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: Compute the indefinite integral of the following function. r(t) = (5 cost,8 sin 7t,9 cos 3t) Select…

A:

Q: (Зу-2 dy 2 y*+2y+17

A: As per the guidelines, I can solve only first question. Kindly repost the question for second…

Q: Evaluate the integral. /2 sin t dt T/4 O a. -0.293 O b. 1.707 O c. 1.507 O d. 0.707 e. 1.207

A:

Q: sin³ydy 1+ cosy A 1+ cosy B 1- cosy (c) siny D sin³y (E) None

A:

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

A:

Q: Evaluate the following double integral (x² cos y – sin x)dxdy. 0.

A:

Q: 4 3. S(3x + 4)%2dx S'4 sin?x dx l sin'x 4.

A:

Q: Evaluate the integral. 4π S t² sin(2t) dt

A:

Q: t sin(t² + 4) dt cos(t² + 4)

A: To evaluate: ∫tsint2+4cost2+4dt Let I = ∫tsint2+4cost2+4dt

Q: Evaluate the following integrals (a) S Cos(2nWt)dt, where W is a constant. n/2 c3 (b) S,"7² S, r²…

A: Integral of cosx is sinx  Integral of sinx is -cosx.

Q: Evaluate the following definite integral. 8y dy y-4y-12 8y dy =D y-4y-12 (Type an exact answer.)

A: Dear student our policy is to answer first one in case of multiple question, so please repost the…

Q: 5. xe*dx 6. S,12 sin?xcosxdx

A:

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

A:

Q: Q2: A. Evaluate the following integrals: 1) S sint cos t dt 3 sin t+5

A: Solution:The given integral is ∫Sint. Cost3 Sint+5dt

Q: Consider the following integrals 5 sin? x i. x² + 6 est dt ii. e3t – 1

A: We have to use comparison test here.

Q: ) Evaluate the following integral: S V2 + sin 3t cos 3t dt

A: We have to find solution of given integral.

Q: Evaluate the following definite integrals: (a) Si (Vi – %) dt (t+1' dt (b) t3 -3 (c) Sm (et – e-t)…

A: According to bartleby guidelines we can answer only the first three subparts of a question.kindly…

Q: Consider the following integrals • * 5 sin? æ i. - dæ x² + 6 e3t dt ii. . est – 1

A:

Q: Evaluate each of the following indefinite integrals. (a) / 12 x²(3x³ – 5)% d (b) / 2t sin(t²)…

A:

Q: e | 8y³ In(y) dy 1

A:

Q: x3 :/ V? +3 dt then If f(x) = 3

A: According to the given information it is required to calculate the definite integral of the…

Q: Compute the following integrals. | cos"(t) sin (t) dt.

A: =?

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: 5. u(x) = sin æ + T/2 sin x cos t u(t)dt.

A: we have to find u(x)

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS: Identif y the u and find du. 1. fa cos² 2t dt 4…

A: 1). Given; I=∫cos22tdt  ...1   We know that; The trigonometric identity: cos2x=2cos2x-1 And…

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

A: Given ∫01cos(x2)dx

Q: Evaluate the following definite integral T/2 I Vcos(x) sin (x)dt. 3

A:

Q: The substitution t tan- is used to find S- %3D de cos 6 Which of the following gives the correct…

A:

Q: Evaluate the following definite integrals. Show your solut 1. S eva -dx 2. So sin³ Od0

A:

Q: Evaluate the following definite integrals, t(1 -t)² dt = а.

A: Solution: ∫-11t(1-t)2dt Expand=∫-11t-2t2+t3dt

Q: (t+ 3)² dt

A: We have to find the integral: ∫t+32t4dt Simplifying using identity a+b2=a2+2ab+b2,…

Q: Solve the following Integral Equation by Method of Successive Approximation: (3) y(x) = 1+A f" sin(x…

A: Given: The integral equation y(x)=1+λ∫0πsin(x+t)y(t)dt.

Q: 1. Evaluate the following integral: Sx? sin x dx

A:

Q: Evaluate each of the following line integrals. (a) х dy — у dx, c(t) = (cos(t), sin(t)), 2n < t < 4T

A:

Q: T/2 cos(z) dz T/6 sin'(z)

A:

Q: 24. Evaluate the integral, if it exists. .2 •5 Vu – 2u? dt b) | y?V1+ y³dy. c) (t – 4) ' a). -du. d)…

A:

Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

Q: Evaluate the following integrals. t? cos(t) dt а. 3x2 – 1 dæ x³ – x + 1 b.

A:

Q: Evaluate the definite integral below. -10r i+16r' j+8t k dt

A: ∫12-10t4 i+16t3 j+8t k dt

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: 8. The definite integral tan? t dt is equal to A. 4 -1 B. 1- c. C. V2+1 D. +1 4

A:

Q: 25. Evaluate the following definite integrals. dy d) (y+2)

A:

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

A:

Q: Evaluate the definite integral. t3 sin (t4) dt %3D

A: We use substitution method

Q: 9. Evaluate the following definite integrals. S" V5x – 1 dx 10 а. b. J sin 2x dx

A:

Q: Evaluate the following integral. T/6 T VI+ cos(6t) dt

A:

Q: Evaluate the definite integral. integral (lower 0, upper 3) t^3 sin(t^4) dt  =

A: We have to solve the definite integral