Definite Integrals Calculator

Enter the expression, variable, and limits of the integral. Use * to indicate multiplication between coefficients and variables. For example, enter 2*x^2+3*x^(-1)+2, instead of 2x^2+3x^(-1)+2.





Solutions:

Examples:

  • To integrate \(\int_{1}^{2}2x^2+3x-2~dx\), enter 2*x^2+3*x-2, the variable x and the limits 1 and 2.
  • To integrate \(\int_{0}^{10}\frac{1}{3}t^2+\frac{4}{3}t ~dt\), enter 1/3*t^2+4/3*t, the variable t and the limits 0 and 10.
  • To integrate \(\int_{0}^{1}\frac{1}{3x^2}~dx\), enter 1/(3*x^2), the variable x and the limits 0 and 1.

Use this calculator to find the definite integral of various mathematical expressions. You can enter polynomials, trigonometric expressions, exponential expressions, among others.

How to use the definite integral calculator?

Step 1: Enter the expression to be integrated into the first input box. Consider the recommendations of the following question to enter the expression correctly.

Step 2: Enter the variable for which to integrate into the second input box. In most cases, the variable is x.

Step 3: Enter the limits of integration in the “From” and “To” boxes. You can enter numbers or constants like e or π.

Step 4: Click “Integrate” to get the definite integral of the entered expression.

Step 5: The result along with the entered integral will be displayed at the bottom.

How to enter expressions in the calculator?

To integrate functions correctly, we only need to input the expression on the right side of the equals sign. This means that if we have the function f(x)=x+1, we must input x+1.

It is important to use the * sign to indicate multiplication between coefficients and variables. For example, we enter 2*x or 4*x, instead of 2x or 4x.

Also, we can indicate exponents using the ^ sign. That is, by entering x^2 or x^3 we indicate that x is being squared and cubed respectively.

Finally, we use the / sign to write fractions. We must use parentheses to indicate the fractions correctly. The following are some examples of how to enter expressions:

  • To integrate \(\int_{0}^{3}x^2+3x+5~dx\), enter x^2+3*x+5, the variable x and the limits 0 and 3.
  • To integrate \(\int_{1}^{5}\frac{1}{5}t^2+\frac{1}{3}t ~dt\), enter 1/5*t^2+1/3*t, the variable t and the limits 1 and 5.
  • To integrate \(\int_{0}^{1}\frac{1}{2x^2}~dx\), enter 1/(2*x^2), the variable x and the limits 0 and 1.

What are definite integrals?

A definite integral has start points and end points, that is, the integral is evaluated over a specified interval from a to b. We find the definite integral by first finding the indefinite integral. We then substitute the upper limit into the integral to obtain a value that must be subtracted by the integral evaluated at the lower limit.

Why find definite integrals?

Definite integrals can be used to find areas, volumes, center points, and other useful data since they are evaluated with specific numbers.

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