Integrals of Polynomial Functions Calculator

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Example

Created on 2024-06-20Asked by Eleanor Harris (Solvelet student)

Evaluate the integral

\int (3x^2 + 2x + 1) \, dx

Solution

To evaluate the integral

\int (3x^2 + 2x + 1) \, dx

: Integrate each term separately:

\int 3x^2 \, dx + \int 2x \, dx + \int 1 \, dx

Use the power rule for integration:

\int x^n \, dx = \frac{x^{n+1}}{n+1} + C

Apply the power rule to each term:

\int 3x^2 \, dx = 3 \cdot \frac{x^3}{3} = x^3

\int 2x \, dx = 2 \cdot \frac{x^2}{2} = x^2

\int 1 \, dx = x

Combine the results:

\int (3x^2 + 2x + 1) \, dx = x^3 + x^2 + x + C

Therefore, the integral

\int (3x^2 + 2x + 1) \, dx

is:

\int (3x^2 + 2x + 1) \, dx = x^3 + x^2 + x + C

Where

C

is the constant of integration. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Samuel Martin on Solvelet

1. Compute the integral

\int_0^2 (3x^3 - 2x^2 + 5x - 1) \, dx

,2. Find the total work done by a variable force

\mathbf{F}(x) = \frac{1}{x}

pounds required to move an object along the

x

-axis from

x = 1

x = 3

using integration.,

DefinitionIntegration of polynomial functions are about finding an antiderivative of expressions of the form ∑anxn. The polynomial is then broken down and integrated term by term seperately by use of power rule of integration. This is one of the basic integrals from calculus and is used in such types of problems as physics, engineering and economics. And possibly a final one that you could not realizes you did not had and will plague your life to never forget this is because the integral of 3x^2 + 2x + 1 is x^3 + x^2 + x + C, where C is the constant

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