Question
Show that if f(x) is integrable on every interval of real numbers,
and if a and b are real numbers with a < b, then
a. f(x) dr and f(x) dx both converge if and only if
S f(x) dr and , f(x) dx both converge.
b. fx) de + f(x) dx = f f(x) dx + f(x) dx
when the integrals involved converge.
View transcribed image text
Expand

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Other

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Estimate the slope of the tangent line at the point indicated. f(x) = lnx; x = 3

A: Slope of the tangent line is the derivative of the given function at the given point. So differentia...

Q: How many revolutions will a car wheel of diameter 30 in. make as the car travels a distance of one m...

A: Click to see the answer

Q: A manufacturer has modeled its yearly production function P (the monetary value of its entire produc...

A: Click to see the answer

Q: Find the general solution of the first-order linear differential equation. dy + 9y = 27 dx %3D

A: Click to see the answer

Q: Find all the second partial derivatives. w =    u9 + v9 wuu  =        wuv  =   ...

A: Click to see the answer

Q: find the domains of ƒ, g, ƒ + g, and ƒ . g ƒ(x) = √x + 1, g(x) = √x - 1

A: Now domain f is the set of all values of x for which, Now domain g is the set of all values of x fo...

Q: What is a cylinder? Give examples of equations that define cylinders in Cartesian coordinates.

A: Explanation: A cylinder is a surface which has straight parallel sides and two round shapes connecti...

Q: Find the area of the region R bounded by y2=a2−ax, y=a+x.

A: Consider the given curves Let sides of the equations are the same. Equate right sides, The limit o...

Q: 1. State whether each of the following integrals converges or diverges: 00 (a) хЗdx (b) х3 dx -2/3 2...

A:  Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the quest...

Q: Write a vector equation for the line segment from P to Q. 4

A: Click to see the answer

Q: Use the initial condition to find the particular solution of the differential equation. differential...

A: Click to see the answer

Q: determine the radius of convergence of the given power series.

A:  

Q: Sketch the region bounded by the graphs of the equations and find the area of the region . y = ex, y...

A: The diagrammatic representation of the area is,

Q: In Exercises 38--45, complete the square and find the minimum or maximum value of the quadratic func...

A: Dear student, since you have posted multiple questions, as per our policy we will answer first quest...

Q: Solve this early. Question no 7 only. But all subparts of question 7 ( a, b, c) .

A: For (a),  

Q: evaluate the integral using the indicated trigonometric substitution, integral (-2x^3/sqrt(x^2+9), x...

A: Click to see the answer

Q: Simplify  exponential expression.   7x5y6 / 28x15y-2

A: Click to see the answer

Q: Find dy/dx by implicit differentiation   y5 + x2y3 = 1 +x4y

A: Click to see the answer

Q: Consider the length h of the perpendicular from point B to side b in the given triangle. Show that

A: The triangle ABC is  We have to prove   ,where  the length h of the perpendicular from point B to s...

Q: Use separation of variables to find the general solution of the differential equation. y- dx 4 cos(T...

A: Click to see the answer

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y ...

A: concept of integral :

Q: by. y=X and yX #3. Find the volume 9in tvat ed the X-axis. on roleting

A: Click to see the answer

Q: Some of the curves corresponding to different values of C in the general solution of the differentia...

A: Click to see the answer

Q: Find lim(y→2) (y^2 − 3y + 1).

A: Click to see the answer

Q: Find ds/dt when θ = 3π/2 if s = cos θ and dθ/dt = 5.

A: Differentiating with respect to t, we get

Q: Find the first partial derivatives of the function. f(x, y) =  7(x − y) x + y fx(x, y) = ...

A: Given: The function  .

Q: Evaluate the definite integral Lx (x² + 1)*dx ,2

A: Click to see the answer

Q: Calculus Question

A: required region is marked in above graph.  

Q: Evaluate the trigonometric function. Round your answers to four decimal places sec 12/5

A: Click to see the answer

Q: Suppose that the intersection of the graph of z=f(x,y)  with the plane x =1 is a parabola that open ...

A: Click to see the answer

Q: a.Find the maximum value of w = xyz on the line of intersection of the two planes x + y + z = 40 and...

A: Given Data The equation is w=xyz. The first equation of plane is x + y + z = 40. The second equation...

Q: Use any of the trigonometric rules we learned to solve the following integrals:

A: Click to see the answer

Q: Find the explicit formula for the general nth term of the geometric sequence described below.

A: Click to see the answer

Q: Plot and label the center, vertices and foci of the ellipse a. 4x? + 32x + 9y² – 54y = -109

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,...

Q: and the parabola the vertical ine The region enclosed by the x-axis y=frx)=3x -x is revolving X=-1 t...

A: Click to see the answer

Q: Find a vector equation of the line tangent to the graph of r(f) at the point Po on the curve. r(1) =...

A: Find the derivative of the function r(t) to find the equation tangent to the graph of the function. ...

Q: Evaluate the integrals using integration by parts. ∫ tan-1 3x dx

A: Now,

Q: Integrate ƒ(x, y) = 1/ (1 + x2 + y2 )2 over a. Triangular region The triangle with vertices (0, 0), ...

A: Given Data The function is f(x,y)=1/(1+x²+y²)².   (a) The triangular vertices are (0,0), (1,0), and ...

Q: Use the initial condition to find the particular solution of the differential equation. Differential...

A: Click to see the answer

Q: determine whether it diverges or converges. If it converges, find the value of the integral

A: To determine if the integral is convergent or divergent.

Q: Need help with this question

A: Given:

Transcribed Image Text

Show that if f(x) is integrable on every interval of real numbers, and if a and b are real numbers with a < b, then a. f(x) dr and f(x) dx both converge if and only if S f(x) dr and , f(x) dx both converge. b. fx) de + f(x) dx = f f(x) dx + f(x) dx when the integrals involved converge.