Find the integral of [ 2x^4 - (4/sqrt(x) ) + 3 ], giving each term in its simplest form

We begin by rewriting it in a more workable form: 2x4 - 4x-1/2 + 3. Indices are easier to integrate than fractions.Now, we integrate each term separately. The first term is 2x4. We increase the power of 'x' by 1, and divide the whole term by it, giving us 1/5(2x5). We then do the same with the second term, giving us -2(4x1/2). The third term doesn't appear to have an 'x' term, but it can be written as 3(x0), x0 being equal to 1. We then do the same to this term, resulting in 3x. As this is an indefinite integral, we add a '+ C' at the end. Our integral is now [ 1/5(2x5) - 2(4x1/2) + 3x + C ]. After simplifying each individual term, our final answer is [ 2/5(x5) - 8x1/2 + 3x + C ]

Answered by Prahlad M. Maths tutor

4016 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate by parts the following function: ln(x)/x^3


Find the Co-ordinates and nature of all stationary points on the curve y=x^3 - 27x, and attempt to sketch the curve


i) Simplify (2 * sqrt(7))^2 ii) Find the value of ((2 * sqrt(7))^2 + 8)/(3 + sqrt(7)) in the form m + n * sqrt(7) where n and m are integers.


How to expand squared brackets?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences