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

• calculusisfun
In summary, the conversation discusses solving an equation involving an integral, specifically the equation integral of f(t)dt from 0 to x = 1. The homework equations provide a piecewise function for f(x) and the attempt at a solution involves manually computing the integral with a guess and check method. The final answer is 1.06484 correct to one decimal place.
calculusisfun
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?

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 you use a spreadsheet use hundreds of term.

## 1. How do I solve an equation involving an integral?

Solving an equation involving an integral involves finding the antiderivative of the function inside the integral. This is done by using integration techniques such as substitution, integration by parts, or partial fractions.

## 2. What is the purpose of finding the integral of a function?

The integral of a function is used to find the area under the curve of the function. It can also be used to solve problems involving motion, volume, and other real-world applications.

## 3. Can the integral of a function ever be negative?

Yes, the integral of a function can be negative if the function is below the x-axis. In this case, the area under the curve of the function will be subtracted from the total area, resulting in a negative value.

## 4. What is the difference between definite and indefinite integrals?

A definite integral has specific limits of integration and gives a numerical value as a result. An indefinite integral does not have limits and gives a general formula for the antiderivative of a function.

## 5. What are some common mistakes to avoid when solving an equation involving an integral?

Common mistakes when solving an equation involving an integral include forgetting to add the constant of integration, using incorrect integration techniques, and making errors in algebraic manipulations. It is important to double-check your work and practice regularly to avoid these mistakes.

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