Welcome to Live Chat

Welcome to LiveWebTutors Services, World's leading Academic solutions provider with Millions of Happy Students.

Call Back
logo

24x7 Support Available

To Get the Best Price Chat With Our Experts

chat now

In A Hurry? Get A Callback

icon
Table of Content

Arbitrary constant of integration


Let us assume a mathematicsfunction F (x) is an integration of a function f (x), then the set of all integrals of f (x) is given by F (x) + cwhere, c be any real constant. Thatmeans a function has single derivative but multiple integrals.Reason behind the arbitrary constant is we know that the derivative of a constant function is zero. According to the second fundamental theorem derivative of the integral of a function is a function itself.Let us consider a function f(x).Integral f (x) = F (x) + c according to the definition of integral.d/dx integral f(x) dx = d/dx F(x) + d/dx c = F’(x) + 0since F’(x) = f(x) we get, d/dx integral f(x) dx = f(x)once we get one integral of a function we can find set of all integrals by adding or subtracting different constants to the integral.

For example; integral of sin x dx = -cos x + c. Here ‘c’ can have any real value.Since, integral of sinx dx = -cos x + c , derivative of –cos x + c will return a function sin x for any value of ‘c’.Let us try the same for c = 0, -1 and 2. At c = 0, d/ dx –cosx = - (-sin x) = sin x and at c = -1, d/dx [-cos x – 1] = d/dx –cos x – d/dx 1 = - (-sin x) – 0 = sin x. Now at c = 2, d/dx [-cos x + 2] = d/dx –cos x + d/dx 2 = - (-sin x) + 0 = sin x. We get same derivative function as derivative of a constant term is always zero.Hence for integrals of any function we get a set of functions which differ by a constant term always.

Integral f(x) dx = F(x) + c1 = F(x) + c2. Here the difference between two integrals is abs (c1 – c2). Hence we get multiple integrals for f(x) as: F(x), F(x) + c1, F(x) – c1….. and so on.Here ‘c’ is called as the arbitrary constant of integration or integration constant.It plays a vital role while finding indefinite integral, since it represents a set of all possible integrals for a given function f (x).Arbitrary constant in definite integral:Definition of definite integral: integral from x = a to x = b f(x) dx = F(b) – F(a). We don’t use arbitrary constant in definite integrals as it is zero or already known in this case.Since we have two bounds of integral we have enough information to solve integral for a constant. Thus there is no need to put ‘c’ while finding definite integrals.F(b) – F(a) suggests that two integrals of f(x) at x = a and x = b differ by a constant value.

Our Amazing Features
  • On Time Delivery

    There is no deadline that can stop our writers from delivering quality assignments to the students.

  • Plagiarism Free Work

    Get authentic and unique assignments by using our 100% plagiarism-free services.

  • 24 X 7 Live Help

    The experienced team of Live web tutors has got your back at all times of the day. Get connected with our customer support executives to receive instant and live solutions for your assignment problems.

  • Services For All Subjects

    We can build quality assignments in the subjects you're passionate about. Be it Engineering and Literature or Law and Marketing we have an expert writer for all.

  • Best Price Guarantee

    Get premium service at a pocket-friendly rate. At live web tutors, we understand the tight budget of students and thus offer our services at highly affordable prices.

live review Our Mission Client Satisfaction
  • I ordered my HRM assignment from this platform. The solution helped me to pass my assessment with flying colors. Well done! Keep up the good work.

    27 Oct 2020

    Arnisa

  • Recently, I ordered my history case study from this platform. The professionals did great work with the content. I am yet to be graded for it but as far as I reviewed the text I am definitely impressed with the quality provided to me at this price. Thank you for your support.

    27 Oct 2020

    Tammy

  • I got good grades with my nursing assignment, all thanks to the experts of this platform. My writing skills are not that great hence the experts of this portal helped me to pass my program with good grades.

    27 Oct 2020

    Sidorela

  • I ordered my English assignment from this platform. The service was very quick and impressive. The customer support executives were very polite and helpful. I am grateful for their assistance.

    27 Oct 2020

    Jenny

  • Overall, it was a pleasant experience. I ordered my management thesis from this platform. The experts did thorough and detailed work on my assignment. All my instructions were implemented precisely.

    27 Oct 2020

    Fiona

View All Review