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 integrable on [0, 1]?

Q: Determine weather the statement is true of false. Explain your answer.

A: Consider the given differential equation dydx=1x2+1 Use separation of the variable method to find…

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

A:

Q: Use the limit definition of definite integral in the form of f(æ) dæ = lim {(#:)Ax, i=1 6 - a and r;…

A:

Q: 30. Find the continuous function f(t) satisfying csin z for all r. 2+ f(t)dt = sin2015 /3

A: According to Leibnitz rule:

Q: Let f(x) dx = -2, f(x) dx = -7, g(x) dx = 9, g(x) dx = -5, Use these values to evaluate the given…

A:

Q: Let H(x) integral ,for -2 ≤ x ≤2.Find the value of s such that H(x)= sH(-x).

A:

Q: Suppose that f(x) has a continuous derivative, (T/2 f(-т/2) — 0, f(T/2) = T/4 and dx = 3. %3D 7/2…

A: Given that:

Q: | (sec 4x – 1)dx

A:

Q: 4. Use the definition of the Riemann integral to evaluate f(x) dx where (a) f(x) = x². (b) f(x)= 3x…

A:

Q: Let | f(x) dx = -9, f(x) dx = 8, g(x) dx = 9, g(x) dx = 15, Use these values to evaluate the given…

A: As per the question, we are solving only the red circled question, that is, part (d). We need to…

Q: If f : [0,2] → R is defined by f(x) = 1 if 0 ≤ x ≤ 1, f(x) = 2 if 1 < x ≤ 2. Show that f is…

A:

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

A:

Q: Let f be the function defined by S1+x, when 0<x<}, }<x<1 0, when x-1. f(x)= Show that fis integrable…

A: Recall the Result/Theorem A bounded function f which has only a finite number of points of…

Q: Find the Fourier integral of f(x) = e-k* when x>0 and f(-x) = f(x), hence prove that cos(wx) dw w…

A:

Q: If f : [0,2] → R is defined by f(x) = 1 if 0 ≤ x ≤ 1, f(x) = 2 if 1 < x ≤ 2. Show that f is…

A:

Q: Evaluate the integral, if it exists.

A: Given: ∫-π4π4t4 tant2+costdt

Q: dx 2 -o x+4x+5

A: The general form of a complex number is given by , where a, b are two real numbers and . Any complex…

Q: Suppose that f(x) > 0 on [0, a], ƒ(x)< 0 on [a, b], ſo“ f(x)dx = 7, and S" f(x)dx = –3. Evaluate the…

A:

Q: An improper integral J converges if : e-x dx Ocr0

A:

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: Compute f'cx) of ×そ9 O f(x)- X-3 at X, = 3 の f(x)= x*+ ラメ+ タメ+1 at Xo=-2 f(x)= 4cos x + 2 sinx at X=…

A:

Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

A:

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: 12. Suppose that g is integrable and that g(x)dx = -7 and [8(x)dx = 2. d: g(x)dx

A:

Q: Evaluate the integral f 2x (x2 + 7)° dx using the substitution u = x2 + 7. 2.x (x² + 7)° dx +C

A:

Q: Find the local linear approximation of f(x) = In(5 + x) at xo = -4. %3D In(5 + x)

A:

Q: Let H(x) integral ,for -2 ≤ x ≤2.Evaluate H'(1).

A: We have given Hx=∫0x4-t2dt We have to calculate H'(1)

Q: c) Suppose fand g are integrable and that S(x)dx = 4 , [ f(x)dx= 6 , [ g(x)dx= -2. Find the…

A:

Q: f (x) = = cos 2x; [0,T] G and

A: topic - mean value theorem

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

A:

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

A:

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…

A:

Q: Let f be a function defined for t 2 0. Then the integral

A: From the graph f(t) = 1-t and LAPLACE TRANSFORM is given as     Lft = ∫0∞e-stftdt

Q: Determine the indefinite integral. S()dx O x+c O 2/x +c O 3 3/x³ + c 2x² + c

A:

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

A:

Q: Evaluate the integral f (t* In ti+ 3t° sin (t*) j + ) dt. (x+1) -2

A:

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: If ƒ is continuous and f(t) dt = 16, find the integral

A:

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: Define (a) P.T. f(x) 0. (b) P.T. f(x) = x+1 [*** sin(1²) dt x 2x f(x) = cos(x²) - cos[(x + 1)²]…

A: Note: As company policy, we solve first three sub-parts only. Please resubmit the remaining…

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…

A:

Q: 2. Calculate the following transcendental integrals: a) S² exee* dx X b) S (x²+1)In (x²+1) dx cos…

A:

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

A:

Q: Find any value of c for which the improper integral cx + 36 x2 + 1 9. da x (4 x + 5) converges.

A:

Q: 3 Suppose that f(x) dx = 7, | f(x) dx = 5, and | f(x) dx = 10. %3D Evaluate the following definite…

A: (a) The given integral is: I=∫35f(x)dx As we know from the integral theorem,…

Q: Let f(x) = x³+1, x<1 1 X+4 5 1.8976 x≥1 Use the composite Simpson's rule to approximate the integral…

A: Introduction: The formula for Simpson's 1/3rd rule is given by,…

Q: Evaluate the improper intergal 1 dx using the residue (x² + 1)3 theorem.

A:

Q: Expand the function f(x) = tan x up to the first two non-zero terms in the Taylor's polyno- xn+1…

A:

Q: ) Let f(x) = cos(x) ln (1+ ax 1+bx, 1 1 2'2 If f(x)dx = 0 where a and b are real be integrable on…

A: