Symbolab Integral Calculator Definite
'/%3E%3Ccircle cx='48' cy='39' r='19' fill='%23f2c9a5'/%3E%3Cpath d='M27 35c3-16 39-17 42 2-8-8-27-9-42-2z' fill='%23374151'/%3E%3Cpath d='M21 86c5-24 49-28 56 0z' fill='%232563eb'/%3E%3Ccircle cx='41' cy='41' r='2' fill='%23111827'/%3E%3Ccircle cx='55' cy='41' r='2' fill='%23111827'/%3E%3Cpath d='M42 52c4 3 9 3 13 0' stroke='%2392400e' stroke-width='3' fill='none' stroke-linecap='round'/%3E%3C/svg%3E)
Reviewed by Calculator Editorial Team
The Symbolab Integral Calculator Definite helps you compute definite integrals with step-by-step solutions. Whether you're solving calculus problems for homework or professional work, this tool provides accurate results and detailed explanations.
What is a Definite Integral?
A definite integral calculates the exact area under a curve between two specified points on the x-axis. It's represented as:
Where:
- f(x) is the integrand (the function to be integrated)
- a is the lower limit of integration
- b is the upper limit of integration
Definite integrals have practical applications in physics, engineering, economics, and many other fields where accumulation of quantities is important.
How to Use Symbolab Integral Calculator
- Enter the integrand function in the input field (e.g., x² + 3x)
- Specify the lower limit (a) and upper limit (b)
- Click "Calculate" to get the result
- Review the step-by-step solution and graph
Symbolab provides both numerical results and symbolic solutions when possible. For complex integrals, you may see an approximate numerical answer.
Formula
The fundamental theorem of calculus connects definite integrals with antiderivatives:
Where F(x) is the antiderivative of f(x).
Worked Example
Let's calculate ∫13 (2x + 5) dx:
- Find the antiderivative: ∫(2x + 5) dx = x² + 5x + C
- Evaluate at the bounds: (3² + 5×3) - (1² + 5×1) = (9 + 15) - (1 + 5) = 24 - 6 = 18
The exact area under the curve from x=1 to x=3 is 18 square units.
FAQ
What types of functions can Symbolab integrate?
Symbolab can handle polynomial, trigonometric, exponential, logarithmic, and many other common functions. For very complex functions, it may provide numerical approximations.
Is the result always exact?
Symbolab provides exact results when possible. For integrals that can't be expressed in elementary functions, it will give a numerical approximation.
Can I use Symbolab for calculus homework?
Yes, Symbolab is an excellent tool for checking your work and understanding the steps involved in solving definite integrals.