Question

I need helping evaluating the following integral:

Integ. ((5x + 4)^(1/2))dx, from x=0 to 1

I am getting something different from what WolframAlpha says it should be equal to be, but I don't know where I'm going wrong. Would anyone be willing to solve this one themselves, and cross their work with mine?
I got: 19/5
WolframAlpha: 38/15
Any and all help is greatly appreciated! :)

Answer 1

To be clear, this is what you want?

\[\int\limits_{0}^{1}\sqrt{5x+4}dx\]

Answer 2

Yes! :)

Answer 3

For the definite integral I get 4*(5*x + 4)**1.5/30 using formal methods (sympy, a Python library). Setting this expression to i(x) and evaluating i(1.)-i(0) yields 2.533333333333327, which is the W-A result.

Answer 4

I used u-substitution, setting u = (5x+4). Can you help me verify the accuracy of my steps with that method? :)

Answer 5

u = (5x + 4)
du = (5x^(1-1) + (0)) dx
= (5(x^0)) dx
= (5)dx
dx = (1/5)du

So.... 1/5(integ.) u^1/2 * du is what I get for the integral, after u-sub, and before taking the anti-deriviative and plugging the numerical value of u back in.

Answer 6

At that point This is what I did...

1/5(u^(.5 + 1)) = 1/5(u^(3/2))
= 1/5(5x + 4)^(3/2)
Plugging in the limits...
= [1/5(5(1) + 4)^(3/2)] - [1/5(5(0) + 4)^(3/2)]
= [1/5(9)^(3/2)] - [1/5(4)^(3/2)]
= [1/5(27)] - [1/5(8)]
= [27/5] - [8/5]
= 19/5
= 3.8
Where am I going wrong?? :/

Answer 7

Please see attached. To be evaluated from upper limit of 9 to lower limit of 4.

Answer 8

Quick read : have you rewritten the limits of integration in terms of u?

Answer 9

...the limits?

Answer 10

x goes from 0 to 1, so what will u do?

Answer 11

Is that it? I will be away for a while.

Answer 12

Well, with u-sub, doesn't one plug in the values of the limits to the "anti-derived" integral, with u plugged back in? This done by subtracting the quantity found using the lower from the quantity found using the upper?

Answer 13

We're probably talking about different approaches. Once you have transformed from x to u you need not return to x, as long as you transform all parts of the original integral in terms of u. In this case, dx becomes du/5; the integrand becomes simply the square root of u; the limits of integration become 4 and 9 (rather than 0 and 1).

Answer 14

At that point This is what I did...

1/5(u^(.5 + 1)) = 1/5(u^(3/2)) ******************************************
= 1/5(5x + 4)^(3/2)
Plugging in the limits...
= [1/5(5(1) + 4)^(3/2)] - [1/5(5(0) + 4)^(3/2)]
= [1/5(9)^(3/2)] - [1/5(4)^(3/2)]
= [1/5(27)] - [1/5(8)]
= [27/5] - [8/5]
= 19/5
= 3.8
Where am I going wrong?? :/

Answer 15

mistake in that line, rest everything looks perfect

Answer 16

you forgot to divide (.5 + 1)

Answer 17

I don't know what BillBell was talking about...

Answer 18

\(\large \int u^{\frac{1}{2}} du = \frac{u^{\frac{1}{2}+1}}{\frac{1}{2}+1}\)


right ?

Answer 19

Ah... Right *whoops!

Answer 20

If I could double-fan you, I would!

Answer 21

so that 3/2 in the denominator is missing all the way to the end...
to fix ur answer, simply multiply ur final answer by 2/3

Answer 22

Thank you soo soo much !

Answer 23

np :) u will be seeing @BillBell 's method shortly i guess whenever ur professor takes time to explain it lol...

Answer 24

Thank you again!