Integral Problem

nate12o6

New member
Joined
Jan 15, 2020
Messages
1
Hi everyone,

Its been about 12 years sense i took my calc courses but am running into a problem that I am trying to figure out.

If I have the value of an integral is there any way to solve for a variable that makes up the integral.

Here is an example:

My integral (Not sure how to format this) is from 0 -> 541 f(t)dt =10817/((1+((1.6)(d)(t)))^(1/1.6) which equals 370,367. I am trying to solve for d.

I have attached a picture that formats the formula i bit better.

1579145565544.png

Again. Trying to solve for d when i know the integral is equal to 370,367.

Thanks for any help!
 

MarkFL

Super Moderator
Staff member
Joined
Nov 24, 2012
Messages
2,953
Hello, and welcome to FMH! :)

I"m going to change \(d\) to \(a\) to avoid confusion and write:

\(\displaystyle 10817\int_0^{541} \frac{1}{\left(1+\frac{8}{5}at\right)^{\frac{5}{8}}}\,dt=370367\)

\(\displaystyle \int_0^{541} \frac{1}{\left(1+\frac{8}{5}at\right)^{\frac{5}{8}}}\,dt=\frac{370367}{10817}\)

Let:

\(\displaystyle u=1+\frac{8}{5}at\implies du=\frac{8}{5}dt\)

And our definite integral becomes:

\(\displaystyle \int_1^{1+\frac{4328}{5}a} u^{-\frac{5}{8}}\,du=\frac{2962936}{54085}\)

Can you proceed?
 
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