Since f(x) =1/x is continuous on (0, 1), f(x) is integrable on (0,1).

Q: Define f(x) = x if x is rational and f(x) = 0 if x is irrational. Compute So f dx and ſ f dx. Is f…

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Q: 2. Let f and g be integrable functions such that f(x) dx = 6 and g(x) dx = –2. Using the Linearity…

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Q: Find the solution in the form of Fourier integrals: Ut- 3uxx = 0, u(0, t) = 0, |u(x, t) bounded as x…

A: As per the question we are given a initial boundary value problem as : ut - 3uxx = 0 And we have to…

Q: What is the resulting integrable form of evx+I x+1

A: We have to find value of given Integral.

Q: suppose f is continuous on [0,1]. Then the integral ∫ab f(x)dx is an area so it must be positive.…

A: If f(x) is below x-axis, then the area ∫ab f(x)dx can be negative.

Q: | (sec 4x – 1)dx

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Q: Define stpes to obtain the general solution of a 2nd order homogeneous ODE with real coincident…

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Q: Let H(x) integral ,for -2 ≤ x ≤2.Evaluate H'(2).

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Q: sho w that fQ) = x xE To,1] is Riemann integrable amm

A: The given function is: fx=x3, x∈0,1

Q: Evaluate the integral using formula 35 (from the 1-page differentiation & integration formula) by…

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Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by = - 2n…

A: The fourier integrals of two continuous fx and gx defined on ℝ are defined…

Q: f(x)=0 for x EQ and f(x)=x otherwise. We can conclude f is not integrable on [-1,1] sim

A: In this question we will use basic concepts of calculus i.e concepts of integration and continuity.…

Q: Which of the following is always true for integrable functions f and g? OSrw-dw]dx= [otwiax- frimax…

A: For integrable functions f and g

Q: D (x) is not integrable on [0,1]

A: Note: Here we are solving 1st problem for the next problem please submit the question again. Given:…

Q: The tangent function f (x) = tan x is integrable from 0 to T. O True O False

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Q: ex What is the integrable form of dx? e* - e -X

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Q: Show that I¿(f) = 1, and conclude that f is integrable on

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Q: Let f be Riemann integrable on J and let f(x) > 0 for x € J. Show that

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Q: Every function which is Riemann 0/3 integrable on [a,b] is continuous. * True O False

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Q: • Compute for the value of constant (C) by solving the given DE using integrable combination. Let…

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Q: Suppose f is Reimann integrable on [a,b]. If f (x)< 0 for all x E [a, b], then S f(x)dx

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Q: Suppose that f and g are integrable and that -1 f(x) dx = 5 h(x) dx = 4 7, dx = %3D Use the rules to…

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Q: Suppose that f is integrable and that So f(z) dz = 3 and So f(2) dz = 7. Find %3D | f(2) dz b. f(t)…

A: Here given as ∫03fzdz=3 and ∫04fzdz=7 (a) Now  ∫04fzdz-∫03fzdz=∫34fzdz Thus ∫34fzdz=7-3=4

Q: (10) Is the line integral ſc f(2)dz always vanishing for all holomorphic functions f on ID, where C…

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Q: Evaluate the line integral ∫(AB) xdx+ydy+zdz using the fact that the integrand is a perfect…

A: Here we find ∫(AB) xdx+ydy+zdz,   by using the fact that the integrand is a perfect differential. A…

Q: Find the total differential of z= f(x, y), where f(x, y) = In Use * for multiplication of variables,…

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Q: Suppose f> 0 is integrable on [a, b], continuous at xo € [a, b], and f(xo) > 0. Prove that f>0.

A: Given f≥0 is integral on a,b continuous at x0∈a,b and fx0&gt;0

Q: If F(z)dz f(t)dt, what are the bounds of integration for the first integral? and

A: Given  ∫abfxdx=∫−8−1fxdx+∫−11fxdx−∫−8−5ftdt

Q: Are the following functions Riemann Integrable to their corresponding in- tervals? Explain your…

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Q: If f(x) is continuous function on la,b] than is not integrable [a,b]. on Select one: O True O False

A: Topic:- function

Q: Is the function f(x) = ( 1, x not equal 1)             ( 0, x equal 1) integrable over the interval…

A: Here, we will show that the given function is integrable. Let us take a point c ∈ (0,1).

Q: Suppose that f and g are integrable and that f (x) dx : :-1 | f(x). h(x) dx = 4 Odx = 5 Use the…

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Q: Let f be an integrable function on [-1,3], with the property that for each E [-1,3], we have | F(t)…

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Q: What is the integrable form of et dr? ex – e -x [(1-u²) ² du O Swi-) - 1) 2 du (1- " (D 2 du

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Q: Show that f(x) = x² is integrable on [a,b].

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Q: Show that if f is Riemann integrable on [a,b] and f(x) ≥ 0 for all x ∈ [a,b], then

A: A bounded function on a compact interval [a, b] is Riemann integrable if and only if it is…

Q: Show that, if f and g are Reimann integrable on [a, b] then f - g is Reimann integrable on [a, b],…

A: We have to prove that following identity.

Q: Are the following functions Riemann Integrable to their corresponding in- tervals? Explain your…

A: Given: g(x)=lnxif x&gt;00if x≤0 To check: Whether the given function is Riemann integrable on 0, 2…

Q: Let H(x) integral ,for -2 ≤ x ≤2.Evaluate H(0).

A: Consider the given integral, Hx=∫0x4-t2dt use the substitution method to solve the above integral as…

Q: Suppose that f and h are integrable and that f(x) dx = -1, f(x) dx = 5, h(x) dx = 4. Use the rules…

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Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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Q: Let f(x) = (cosh x)² be defined on (0, 0), find %3D d 1/2) . dy

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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: Find and explain an example of a Riemann Integrable function that does no have an antiderivative.

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Q: Compute the line integral of F = (-y, x) along the line segment from (0,0) to (1,1).

A: The line integral is evaluated using the following formula  ∫cF→x,yds=∫abF→rtr'tdt    , a≤t≤b   ,…

Q: Suppose that f and h are integrable and that: i fx) = -1, f(x) dx = 5, h (x) dx = 4 ,Find: a. S–2…

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Q: F is Riemann integrable on IFI is Riemann integra ble

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Q: Let f be the function defined by fx)=1+x, when 0<x<}, }<x<1 0, when x . Show that fis integrable…

A: We know that  A bounded function f which has only a finite number of points of discontinuity in…

Q: Let 2 C = sin dx. As f(x) = sin(1/x) is continuous except at 0 and bounded, f is integrable on…

A: C=∫-11sin1x2dx=-∫-11sin2uu2du is correct because the value of the integral ∫-11sin2uu2du is…