# Definite Integral Calculator Problem

• poiboi86
It is important to note that when using calculators, it is important to make sure the settings are correct and that you are using the correct method for solving the integral. It is also helpful to double check your work by solving the integral by hand as well. In summary, the correct answer for the definite integral 4π∫{0,3/2}(x^3)dx is 81π/16 and it is important to check the settings and method when using calculators.
poiboi86
Hi.

## Homework Statement

I'm solving the definite integral 4π∫{0,3/2}(x^3)dx

For some reason I get a different answer solving by hand and using my TI-89 than I do when I use an online calculator or my TI-36X Pro. I have to use the TI-36X Pro to take my Engineering FE exam in 2 & 1/2 weeks and need to know why I'm getting these different answers.

Does anyone see what I'm missing?

## The Attempt at a Solution

Solving by hand I get πx^4|{0,3/2} = π(3/2)^4 - 0 = 81π/16

This is also what the solution shows, and what my TI-89 calculator gives me as an answer.
But for some reason when I type that same integral into my TI-36X Pro calculator, or an online integral calculator like: <http://www.solvemymath.com/online_math_calculator/calculus/definite_integral/index.php>
I get the answer 15.904 which is 5π/16.

Thank you very much!
Isaac

Last edited by a moderator:
The first answer is correct. 81π/16=15.90431. 5π/16=0.98174. I don't think there is anything wrong the calculators.

## What is a definite integral calculator?

A definite integral calculator is a tool used to evaluate definite integrals, which are mathematical expressions that represent the area under a curve, between two points on the curve. It essentially calculates the total area between the curve and the x-axis within a specific interval.

## How does a definite integral calculator work?

A definite integral calculator uses numerical methods, such as the Riemann sum or Simpson's rule, to approximate the area under the curve. It divides the interval into smaller subintervals and calculates the area of each subinterval, then sums them up to get an approximation of the total area.

## What are the benefits of using a definite integral calculator?

Using a definite integral calculator saves time and effort in calculating integrals manually. It also provides more accurate results compared to manual methods. Additionally, it can handle complex integrals that may be difficult to solve by hand.

## Are there any limitations to using a definite integral calculator?

Definite integral calculators can only approximate the area under a curve and may not provide exact solutions. They also have limitations in handling certain types of integrals, such as those with discontinuities or infinite bounds.

## How can I use a definite integral calculator effectively?

To use a definite integral calculator effectively, it is important to have a good understanding of the concept of integration and the different methods used to approximate integrals. It is also helpful to check the calculator's settings and make sure it is using the desired method for approximation. Additionally, it is recommended to double-check the results with a manual calculation or using a different calculator.

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