Integration Problems... Can someone please tell me where I'm going wrong?

Question

I'm currently revising questions on integration regarding definite and indefinite integrals.
I know HOW to integrate - but when subsitituting each of the limits into the new formula then subtracting them from each other I always seem to get a different answer than what's on the markscheme.

For example one question was: (the S is supposed to stand for the integral symbol)
Find S (x^3 - 10x^2 +28x) dx with limits 3 and 0

I get this bit ok: x^4/4 -10x^3/3 + 28x2/2
So I replaced x for 3 and eventually got to 81/4 - 90 + 126. I took 0 away from this.
But first I wanted to simplify 81/4 - 90 + 126, so I converted the 90 to 360/4 and the 126 to 504/4 and got the answer -63/4 as opposed to the actual answer of 56 and 1/4.

Can someone please point out where I am going wrong. Am I not supposed to convert them into fractions?
Thank you so much in advance :)

Answer 1

Everything is correct, but you just made an arithmetic error.



Your conversions were correct (360/4, 504/4), and the sum of the numerators should have been 225.



Dividing by 4, you should get 56.25 which is 56 and 1/4.



It's probably just an arithmetic error.

Answer 2

81/4 - 360/4 + 504/4 - 0 = -279/4 + 504/4 = 225/4 = 225/4 = 56 and 1/4

Answer 3

curve passes by using (-4, 9) and is such that dy/dx = a million/2x^3 + a million/4x + a million. discover y in terms of x. you should get after integration y = (a million/8)x4 +( a million/8) x^2 + x + C Now, replace in -4 for x and 9 for y and resolve for C 9 = 32 + 2 - 4 + C C = 9 - 32 - 2 + 4 C = -21 So, the integrated function with the right consistent is y = (a million/8)x^4 + (a million/8)x^2 + x - 21