Explain the meaning of the integral ∫∫S (∇ x F) ⋅ n dS inStokes’ Theorem.

Q: Evaluate the double integral f(r, 0) dA. ' π/2 re dr de

A:

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4x(1 – x² )dx = i

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 5 4x(1 – x² )dx = i

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. | 4x(1 – x² )dx = i -1

A:

Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) -5t- dt. If the integral does not…

A:

Q: Explain the meaning of the integral ∮C F ⋅ dr in Stokes’ Theorem.

A: Let S be a piecewise smooth oriented surface with a boundary that is a simple closed curve C with…

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. La (12…

A: According to the given information, it is required to evaluate the integral.

Q: Define f : [0, 1]→R by f(x) = x. •1 Use the definition of the integral to prove that 1 x dx |

A: Definite integral: An integral that contains the upper and lower limits then it is a definite…

Q: Compute The double integral of a function f(x, y) = 73 over a rectangle [2, 4] × [3, 6]

A: To compute the double integral of a function fx,y=73 over a rectangle 2,4×3,6

Q: Evaluate the integrals in Exercises using integration by parts

A: Solution of the given integrations can be found with the help of the integration formulas and…

Q: x +1 dx. Vx² + 10x + 28

A: given∫x+1x2+10x+28dxlet us write numeratorAddx(x2+10x+28)+B=x+1A(2x+10)+B=x+12Ax+10A+B=x+1comparing…

Q: Using only the definition of RS-integral, evaluate .2 x* d[x}.

A:

Q: Je t ež cos (2t)dt

A:

Q: Prove from the definition of the Ito integral that sdW, = tWt – | W,ds.

A: To prove the below statement using the definition of integration. ∫0tsdWs=tWt−∫0tWsds

Q: Use the fundamental theorem of calculus part 2 to evaluate the 3 integral: (8 sin x) dx. Noto: Round…

A: Our Aim is to evaluate the integral given below:-∫π/4π/3 (8 sin x) dx -(i) using Fundamental Theorem…

Q: Using only the definition of RS-integral, evaluate 2 |x* d[x}.

A:

Q: Use the definition of the Riemann integral to show that f is Riemann integrable in [-1, 1] and…

A: In this question, we check the function is Riemann integrable and then evaluate the definite…

Q: Use Green's theorem to determine the value of the integral where the curve x2 + 4 = 1 traveled…

A:

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A:

Q: Using only the definition of RS-integral, evaluate 2 ,2 x* d[x}.

A:

Q: Evaluate the integrals in Exercises using integration by parts.

A: Integration of a function is the process of finding the anti-derivative of the function. The…

Q: Evaluate the integrals in ∫esec πt sec πt tan πt dt

A: Given: ∫esecπtsecπttanπtdt for evaluating this integral we substitute esecπt=u now differentiating…

Q: Identify the type of generalized integral +00 fx'e* dx- and in continuity (if converging) to be…

A: According to question,Given Integral,Let I= ∫0+∞ x2ex3 dx

Q: Evaluate the integrals in Exercises using integration by parts

A: Since you have posted more than one question, we answer the first question for you. For the other…

Q: F(x) = sin(t) dt %3D 3x

A:

Q: Evaluate the integral: fnste" du ds dt

A:

Q: Evaluate the integral in terms of u. sinh u• du = + C %3D 3.

A:

Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: Given: ∫0π4 sec2θ dθ To solve: The integral by using Fundamental Theorem of Calculus.

Q: Use Part II of the Fundamental Theorem of Calculus to evaluate the integral. So (cx³ + dx² + e) dx…

A:

Q: Evaluate the integral. inegral  1 / (x+a)(x+b) dx

A: 1x+ax+b=Ax+a+bx+b   →1 On simplification, we get ⇒1x+ax+b=Ax+b+Bx+ax+ax+b⇒1=Ax+b+Bx+aNow when x=-a,…

Q: Rewrite the iterated integrals in the order dzdxdy 1 1-x² SS S f(x, y, z)dydzdx 1-x 0 0

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 3 | 4x(1 – x² )dx = -1 i…

A: Given that: ∫-134x(1-x2)dx

Q: Using only the definition of RS-integral, evaluate .2 x* d[x).

A:

Q: Evaluate the double integral where D is the triangle bounded by the x-axis, y-axis and the line y =…

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 4x(1 – x²)dx = i -1

A: To find the value of given integral.

Q: (b Set up (but do not evaluate) the given integral in the order da dy dz. Show your work!

A:

Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)

A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…

Q: Evaluate the integral; f, Ni-1, tsin(at)) dt

A: Evaluate the definite integrals  in the following  way:-

Q: (10x – 3x + 1)dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Evaluate the integral, if it exists.    ∫0π/4  (1 + tan t) 3 Sec2 t dt

A: Given information: The integral is ∫0π4+tant3sec2t dt  Calculation: Apply the u-substitution method.…

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 5 | 4x(1 – x² )dx = -1 i

A:

Q: If f(r)dr = f(x)dr+ | f(z)dr - f(r)dr. 7. what are the bounds of integration for the first integral?…

A:

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. (x? 4x…

A: We can find the solution

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 4 | 4x(1 – x*)dx = i -1

A:

Q: Evaluate / F. dr using the Fundamental Theorem of Line Integrals.

A: In this question, we used the fundamental theorem of vector calculus. here first we prove the vector…

Q: obtain a formula for any integral of the form (- a)* dz.

A: Given∫xb-1(cxb-d)kdx

Q: The resulting integral of form --F(0) +C. de has the What should be the value of e to make F(@)=0?

A:

Q: Evaluate the integral using Part 1 of the Fundamental Theorem of Calculus. 2 | 4x(1 – x² )dx = i -1

A: Given,    ∫-124x(1-x2)dx