Definite Integral Calculator Symbolab

Displacement Formula:

\[ s = \int_{a}^{b} v(t)\, dt \]

Displacement (m):

1. What is a Definite Integral Calculator?

Definition: This calculator computes the definite integral of a velocity function to determine displacement over a time interval.

Purpose: It helps students, engineers, and scientists calculate displacement from velocity or solve general definite integrals.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ s = \int_{a}^{b} v(t)\, dt \]

Where:

\( s \) — Displacement (meters)
\( v(t) \) — Velocity function (meters/second)
\( a \) — Lower bound (seconds)
\( b \) — Upper bound (seconds)

Explanation: The integral sums up the infinitesimal displacements over the time interval to find total displacement.

3. Importance of Definite Integral Calculation

Details: Definite integrals are fundamental in physics for calculating displacement, work, and other quantities from rate functions.

4. Using the Calculator

Tips: Enter the velocity function (e.g., "t^2", "sin(t)", "3*t+5"), the lower and upper bounds of integration. The upper bound must be greater than the lower bound.

5. Frequently Asked Questions (FAQ)

Q1: What functions can I enter?
A: The calculator supports polynomial, trigonometric, exponential, and logarithmic functions.

Q2: How accurate are the results?
A: Results are numerically computed with high precision (typically 8-10 significant digits).

Q3: Can I use variables other than t?
A: The calculator expects 't' as the independent variable in the velocity function.

Q4: What if my bounds are reversed?
A: The calculator will automatically swap them and give the negative of the result.

Q5: Can I compute other integrals besides displacement?
A: Yes, this calculator works for any definite integral by interpreting the function appropriately.