Let a and b be real numbers, and let h be a continuous function defined on [a, b]. (a) Change the order of integration to show that h(y) dy dx = (b – y)h(y) dy. a a a

Q: Evaluate the iterated integral. 4z (In(x) xe- dy dx dz J3

A: Formulae used∫e-ydy = -e-y + C∫x2dx    = x33 + C ---------------------------------------- I…

Q: Evaluate the integral. (Use C for the constant of integration.) t3 dt V1- t8

A:

Q: Use the identity f(x) dx = f(x) dx + f(x) dx to compute the integral. %3D -A -A sin(t) dt (Hint:…

A: Explained below

Q: If | f(z)dx f(x)dx + what are the bounds of integration for the first integral? a = and b =

A: Given that ∫abfxdx=∫−47fxdx+∫78fxdx−∫−41fxdx

Q: Evaluate the iterated integral: xy'e-" dx dy

A: Here we evaluate the iterated integral

Q: If {(-)dn = [ f(=)dz + [ 1 f(x)dz what are the bounds of integration for the first integral? a = and…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) dt 1- t10

A:

Q: Evaluate the integral. (Use C for the constant of integration.) t dt + 10

A:

Q: If | f(z)dz = | f(=)da + / f(z)dz – | f(z)dz, a what are the bounds of integration for the first…

A:

Q: d) Evaluate using integration by parts: J(x+ 2)In x dx

A:

Q: The functions f and g are integrable and J f(x)dx = -2, Į f(x)dx = - 8, and I g(x)dx = 3. Use these…

A:

Q: 4. Let f(x) = x, Vx E [0, b]. Show that f is integrable and that 62 f(x) dx : Answer:

A: Given function is  fx=x, ∀ x∈0,b

Q: If f(x)dr f(x)dæ + f(x)dx – what are the bounds of integration for the first integral? a = and b =

A:

Q: Find the total differential. z = x cos(y) – y cos(x) dz =

A:

Q: Compute the line integral of the scalar function f(x, y) = /1 + 9xy over the curve y = x' for 0 < x…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) t3 In(t) dt C must be in capital…

A:

Q: 5. Let F (x, y) = (4xcos(y))ï – (2x² sin(y))j. (4xcos(y))i – (2x² sin(y))j. Find a function f such…

A:

Q: Find the double integral [[ f (x, y)dA for the function f(x, y)=1-6x²y and R:0<x<2,-1 <x< 1.

A:

Q: If {(=)dz = f(x)dx f(x)dx + f(x)da f(x)dx, what are the bounds of integration for the first…

A: Solution:

Q: (c) Let f : [0, 2] → IR be defined by 5 if 0 <a < 1 f(x) := {3 if a = 1 2 if 1 < r < 2 Use…

A: Given that: fx=530≤x&lt;1x=121&lt;x≤2 The integral of the given function on [0,2]. I=∫01fxdx+∫12fxdx

Q: Compute the line integral of the scalar function f(x, y) = over the curve y = x° for 0 <x <1 /1+ 9xy…

A:

Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by sintwa] 2л…

A:

Q: If 3 f(2)dz = f(z)dr + f(x)dr –1, f(2)de, 3. what are the bounds of integration for the first…

A: We have to find a and b

Q: C for the con

A:

Q: (a) Define the principal value integral from a to b of the function f(x), where f (x) has a…

A:

Q: 3. ) Compute for the increment of the function f(x,y) = *+3y . Also, find the total differential of…

A: w = f (x, y) and let ∆x and ∆y be increments of x and y respectively. The increment ∆w of w = f (x,…

Q: c9-x² f(x, y) dy dx as an iterated integral in the Express order dx dy.

A: ∫-33∫09-x2f(x,y)dy dx

Q: 10. Find the bounds of integration a, b, c, d such that f (x, y) dydx f(x, y) dædy.

A:

Q: 3. Suppose that f and g are integrable and that f(x) dx = -1; , f(x) dx = 5; and f, h(x) dx ='4,…

A:

Q: 2 - 4 f(2)dz = / f(x)dx + | f(=)da - f(t)dt, а 9 9 what are the bounds of integration for the first…

A:

Q: Compute the line integral of the scalar function f(x,y)=√1+9xy over the curve y=x3 for 0≤x≤9 ∫c…

A: Given information: The function is f(x,y)=1+9xy over the curve y=x3 for 0≤x≤9 such that ∫c f(x,y)ds.…

Q: f (t)dt = x tan 4 а

A:

Q: Evaluate. (use C for aonstant of intgration) dx 2 X "- 3

A:

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) t2 dt 1 - t6

A:

Q: For a function h and an interval I, the oscillation of h on I is defined by w(h, I) = sup |h(æ) –…

A:

Q: 9. Find the bounds of integration a, b, c, d such that T (a, u) dydar. f(x, y) dædy =

A: x≤y≤4x=y →y=xy=40≤x≤4x=0 to x=4

Q: Express the antiderivative F of f satisfying the given initial condition as an integral. f (x) = sec…

A:

Q: Use the specifie substitution to find or evaluate the Integral. (Use C for the constant of…

A: To solve the integration uisng substitution method

Q: Find the total differential. z = x sin xy

A: Given: z=x sinxy To determine: The total differential of the given function.

Q: Evaluate the integral. (Use C for the constant of integration.) t5 In(t) dt

A:

Q: Consider the integral x³+1 x³(x²+1) -dx What is the correct partial fractio OA Bx + C

A: We have to choose the correct option from the given options according to the given information

Q: Find the double integral ff (x² + y² do, over R={(x, y):-1≤ x ≤ 1,0 ≤ y ≤ 2}. 1.

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

Q: Q1/ Set up the limits of integration for evaluating the triple integral of a function F(x, y, 2) (0,…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS, WE ARE ANSWERING ONLY FIRST QUESTION AS PER…

Q: Let fbe twice differentiable with f(0) = 4 f(1) = 8, and f' (1) = 3 Evaluate the integral o af"…

A:

Q: 4. Find the total differential of z = In(x + y), x= w, y = w². By how much will z change if w…

A:

Q: b) Evaluate the iterated integral In z x e' dy dz dx 3 cx2 1 x,

A:

Q: If f(z)dz = f(x)dæ + f(x)dx 7 what are the bounds of integration for the first integral? a = and b =

A: