How to solve an equation involving an integral? integral of f(x) = 1?

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SUMMARY

The discussion centers on solving the integral equation where the integral of the piecewise function f(t) from 0 to x equals 1. The piecewise function is defined as f(x) = sin(x)/x for x ≠ 0 and f(0) = 1. A user calculated an approximate solution of 1.06484 using a calculator but was encouraged to perform manual computations for accuracy. The recommended approach involves estimating a value for x, performing numerical integration by summing a finite number of terms, and adjusting the guess based on whether the sum exceeds or falls short of 1.

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How to solve an equation involving an integral? integral of f(x) = 1?

Homework Statement


Solve the following equation correct to one decimal place.

integral of f(t)dt from 0 to x is equal to 1

Homework Equations



piece wise function -> f(x) = {sinx/x for x \neq 0 and 1 for x = 0


The Attempt at a Solution


I have no idea how to solve this kind of problem by hand.. I did it on my calculator and got 1.06484

Any ideas?
 
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calculusisfun said:

Homework Statement


Solve the following equation correct to one decimal place.

integral of f(t)dt from 0 to x is equal to 1

Homework Equations



piece wise function -> f(x) = {sinx/x for x \neq 0 and 1 for x = 0

The Attempt at a Solution


I have no idea how to solve this kind of problem by hand.. I did it on my calculator and got 1.06484

Any ideas?

Come on...if they ask you just one decimal it's clear you have to do some manual computation. So...
What is an integral ? It's a sum.
A sum of infinite terms.
Since we don't have an infinite time, we take just a few steps.
Guess a value for x.
Let's say 2, take 10 steps, so 0.2 each step.
Compute the sum.
If it's over or above 1, adjust your guess.
If you use a spreadsheet use hundreds of term.
 

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