Which of the following is always true for integrable functions fand g? x) dx where g(x) + o (B) dr = )dx dr D) )dx

Q: In ir le) secx dx to be integrable using the formula What should be the value of A for 2- sec x…

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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: Evaluate the triple iterated integral. xyz³ dx dy dz

A: ∫02∫02∫-14xyz3dxdydz=∫02∫02x2yz32x=-1x=4dydz…

Q: Evaluate iterated integral.

A: ∫03∫45xx2+3ydydx

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

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Q: | (sec 4x – 1)dx

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Q: (a) Evaluate the indefinite integral (anti-derivative) d.x Vr2 +1 by using the substitution u = x?…

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Q: Evaluate iterated integral.

A: Given, ∫01 ∫36 xx2+3y dx dy

Q: The area of the region between the graphs of y = r and y = -x from x = -1 to r = 0 is .2 %3D %3D…

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Q: Find F'(x), where F(x)= int. of ((t^2)+1)dt, from sin(3x) to x=-4. Use the 1st rule of the…

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Q: Evaluate the iterated integral. 5 (ху) dy dx

A: Topic = Integration

Q: Df be areal value integrable on [0,11 f(x)dx =1. t

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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: • !!! 622 dV where G is bounded by x + 2y + 4z = 8 in the first octant. 3. Evaluate

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Q: X. 2ze-x² dy dx dz

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Given xdy-ydx=4x4dx

Q: Estimate the integral of f(x)=sin(x)/x between 0 and 1 using Trapezoidal Rule with h=0.05.

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Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Evaluate the iterated integral. V1- x4 dy dx

A: The given integration,           ∫01∫0x31-x4 dy dx

Q: Prove the following, assuming f and g to be integrable on [-L,L]. (a) If f is odd, then f(x) dx 0.…

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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: Which of the following is incorrect about the properties of an integral? rx)dx = - L, f(x)dx Si…

A: As we know that from property of definite integration.

Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: to express the integrals as limits of [ f(x) dx (b) [f(x) dx

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Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: Compute the integral fo S x cos(xy)dxdy

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Q: Evaluate the integral [(x+2y)dy.

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

Q: If I, = Sx" cos x dr, by using integration by parts, prove that In = x" sin r + na"- cos r – n (n –…

A: We use integration by parts to show given condition.

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

A: This is a false statement.

Q: Which integral computes arc length of f(x) = x5/2 on [0, 1]? 1 49 -x' dx 1+ 4 - 1 | V1+ x° dx 1 1+…

A: We have to find the arc length

Q: Use (a) the Trapezoidal Rule integral 1to 4    sin x dx                 with n= 5

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

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

Q: f(x) dx = where a < b s c dx =

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Q: Evaluate the improper intergal dx using the residue 2 (x² + 4)² theorem.

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Q: Which of the following is always true for integrable functions f and g? ® S dx =- f(x) g(x) (B where…

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Q: Which of the following is not an improper integral? 1 dx cos x 2 cos x dx | cos x dx 0. 1 dx cos x 2…

A: Given, The definite integrals We have to find the integral which is not improper.

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: is f'(x) given the integral function f(x) = cos(u) sin(u) du?

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Q: e In (x le) (2- secx dx to be integrable using the formula - se What should be the value of A for u"…

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Q: Let f(x) = x² sin – if x # 0 and f(0) = 0. Then ƒ Reimann Integrable True False

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Q: Give the general antiderivative for the integrand in the definite integral (cos +1)dx. cos x

A: Simply integrate and put the limit than simplify.

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

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Q: a) Compute these two integrals shown below using one application of trapezoidal rule and Simpson's…

A: Given that ∫23x dx ∫-66x2cosx dx we have to calculate given integral using  trapezoidal rule.

Q: Find the value of 'h' in 8 dx evaluating by 1+x Trapezoidal rule braking in 24 intervals. 1.25 0.25

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Q: Consider the following theorem. Theorem If f is integrable on [a, b], then FX) dx = lim ° fx;,)ax n-…

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