(§5.4, Q12) Evaluate the integral using FTC I: (5u* + u? – u) du.

Q: Find the product of the integral 1- LL,x? e*ydxdy

A:

Q: Evaluate the integral ∫1/ √tcos (√t+3)dt

A:

Q: 4 1 Replace the letter A in the integral J(2x³ + 4)* dx so that the integral evaluates to (2a3 + 4)°…

A:

Q: 1 J z(9 – In² z}5/2* 피(9-

A: We have to evaluate the given integral.

Q: 2. Use the form of the definition of the integral given in Theorem 4 (p. 380) to evaluate the…

A:

Q: evaluate the integral.

A:

Q: Evaluate the following integral 2dr J z (3(In z)2 + 12 In r- 15)

A:

Q: prove by definition that the integral from a to b of xdx = b^2-a^2/2

A: To Prove:    ∫abxdx=b2-a22

Q: Compute the integral based on 2where g is the cloed cuve 2.

A: In this question, we find the value of complex integral    I=∫γ z-2dz For the given contour.

Q: Evaluate the integral. (u + 5)(u – 6) du

A:

Q: Evaluate the integral.

A:

Q: Evaluate the integral. 1 u' 1 du 5 u

A:

Q: In Exercise, evaluate the given integral.∫5e-2xdx.

A: The given integral ∫5e-2xdx

Q: Evaluate the integral. 7t dt 1 + t2' 1 + t2

A:

Q: Evaluate the integral by making the given substitution. dt u = 1 - 7t (1 – 7t)6' -

A:

Q: Evaluate the integral

A:

Q: Compute the given integral. 11z - 2 11x² - 4x + 5 -dr +C

A:

Q: Evaluate the integral. 1 ds V5s - 9

A: Given,         ∫15s-9ds

Q: Find the area +6 C1 R -6 +6 C2: 4x2 + y² = 16 -6 using green's theorem.

A: We are given the above region of which we need to find the area and as per the instruction, we need…

Q: (b) Evaluate the integral | xln xdx using by parts formula.

A:

Q: 2.3 Use the Cauchy integral formulae to evaluate 22 -1 J (9 – 2ª)(2 + 2i))* where C is a circle |2 +…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Evaluate the integral or show that it is divergent.

A: Introduction -  Evaluating the integral of the given function - f(x) = ∫0112-3xdx f(x) = -∫0113x-2dx…

Q: Use Cauchy's Integral formula, Evalnate the following zl=3 • I = 6 %3D 근 (2-21)2

A: Cauchy Integral formula: If f(z) is a analytic function within and on a closed contour C, and if a…

Q: Use the substitution z = tan (6/2) to evaluate the integrals in Exercises 41 and 42. 42. 41. esc @…

A:

Q: Evaluate the integral.

A: Given:            ∫461t2-9dt

Q: Evaluate the integral using the given substitution. u=8x + 10 /8x+10 A. +C 3/2 8(8x+10)* O B.…

A: Simply integrate

Q: Evaluate the following integrals.

A: Given that, ∫dtt3+1 By using (a3+b3)=(a+b)(a2-ab+b2) ∫dtt3+1=∫dt(t+1)(t2-t+1) First, take a partial…

Q: Evaluate the integral. 4 + u² du u3

A:

Q: 62. dz, C is |z| = 3 C c z² +4

A:

Q: Evaluate the given integral where C is the directed line segment that joins the point 1 to the point…

A: The given problem is to evaluate the given path integral over given path of line segment joining…

Q: Use areas to evaluate the integral. 14b 2s ds, 0<a<b a 14b | 25 ds =0 a

A:

Q: Use areas to evaluate the integral. 11b 2s ds, 0<a<b

A: Consider the integrals, ∫a11b2s  ds,   0&lt;a&lt;b

Q: Consider the following integral 3d.r (16-472)5 A suitable trigonometrie substitution to reduce it to…

A:

Q: Evaluate the integral da (8r +4)' 4)3 by making the appropriate substitution: u= dr (8r + 4)°

A:

Q: Evaluate the integral. 3t-2 clt to t +1

A:

Q: Evaluate the integral. 1 (u + 8)(u – 9) du 0,

A:

Q: Evaluate the integral. 4,3 - 32+ 4 른t) dt

A:

Q: In (a le) (2- sec2x)m sec'x sec ( 3A – x) What should be the value of A for dr to be integrable…

A:

Q: Evaluate the integral. 4 2t 9 -i- j+¬Vt k dt (9+?)*

A:

Q: Evaluate the Integral S Ctan 3 CE>) (sec 3 LE> ) dt

A:

Q: 20 + S 2c + 5 こ

A:

Q: ate the integral by making the giv dt u = 1 – 6t 7: (1 – 6t)*

A:

Q: Evaluate the integral by making the given substitution.

A: The integral given in the question is: u-substitution is: u = 1-6t Taking derivative  du = 0-6dt =…

Q: Evaluate the integral. 18 J xp- 3/2-36 x 18 3/2-36x

A:

Q: Evaluate the integral.

A:

Q: Evaluate the triple integral: -In y (z) dzdydx A. In 4 + 13/6 C. 13/6 - In 4

A: Note:- In this problem, option is not correct. If we take f(x, y, z)=1 instead of z then option (4)…

Q: 3 In 3x Evaluate the defınite integral : J 6x2

A:

Q: If the terms of the AP Ja - x, Vx, Ja +x, . are all integers where ..... .. a >x >0, then find the…

A: Introduction :

Q: Evaluate the integral     ∫     (3/u +u/4)du   =________________________________+ C

A: Given integral cn be written as We know that integral of (1/x)dx=ln(x) and integral of…