Tabular integration Calculator

Ask and get solution to your homeworkAsk now and get step-by-step solutions

Example

Created on 2024-06-20Asked by James Anderson (Solvelet student)

Evaluate the integral

\int x^2 e^x \, dx

using tabular integration.

Solution

To evaluate the integral

\int x^2 e^x \, dx

using tabular integration: 1. **Setup the table:** \begin{tabular}{c|c}

\int x^2 e^x \, dx

& \\ \hline

\frac{d}{dx}

\int e^x \, dx

\\ \hline

x^2

e^x

2x

e^x

2

e^x

0

& \end{tabular} 2. **Form the integral:**

\int x^2 e^x \, dx = x^2 e^x - \int 2x e^x \, dx.

3. **Apply tabular integration again:**

\int 2x e^x \, dx = 2x e^x - \int 2 e^x \, dx.

4. **Combine the results:**

\int x^2 e^x \, dx = x^2 e^x - (2x e^x - 2e^x) = x^2 e^x - 2x e^x + 2e^x.

5. **Result:** The integral

\int x^2 e^x \, dx

is:

x^2 e^x - 2x e^x + 2e^x + C.

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Sofia Mitchell on Solvelet

1. Use tabular integration to estimate the value of

\int_{0}^{1} e^x dx

.2. Approximate the area under the curve

y = x

from

x = 0

x = 4

using tabular integration.,

DefinitionTabular integration is an integration by parts method that specifically works well with products of functions (instead of the generic integration by parts), and is especially useful with repeated integration by parts. It contains the process in a table form. Ex: How to integrate ∫xexdx using tabular integration by writing a table of the derivatives of x and the integrals of ex.

Related Calculators

Numerical value of an algebraic expression Calculator Laplace Transform of Periodic Functions Calculator Fourier Transform of Integrals Calculator Conditional Probability Calculator

Need topic explanation ? Get video explanation