Evaluate.

Integral from nothing to nothing left parenthesis x squared minus 7 x plus 2 right parenthesis font size decreased by 1 font size decreased by 1 dx∫x2−7x+2 dx

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Part 1

Integral from nothing to nothing left parenthesis x squared minus 7 x plus 2 right parenthesis font size decreased by 1 font size decreased by 1 dx∫x2−7x+2 dxequals=enter your response here

It looks like you want to evaluate the integral of the function \( x^2 - 7x + 2 \) with respect to \( x \). 

However, you didn't specify the limits of integration. I will proceed assuming this is an indefinite integral (i.e., no specific bounds are given).

The integral of \( x^2 - 7x + 2 \) is computed term-by-term:

\[
\int (x^2 - 7x + 2) \, dx = \int x^2 \, dx - \int 7x \, dx + \int 2 \, dx
\]

We integrate each term:

1. \( \int x^2 \, dx = \frac{x^3}{3} \)
2. \( \int 7x \, dx = \frac{7x^2}{2} \)
3. \( \int 2 \, dx = 2x \)

So, the integral is:

\[
\frac{x^3}{3} - \frac{7x^2}{2} + 2x + C
\]

where \( C \) is the constant of integration.

If you need this evaluated with specific limits (from \( a \) to \( b \)), please let me know! 

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Would you like any further details or clarification on the solution?

Here are some related questions you might find useful:
1. How do you evaluate a definite integral with limits of integration?
2. What is the concept of the constant of integration in indefinite integrals?
3. How can you check your result for definite integrals using the Fundamental Theorem of Calculus?
4. How do you handle integration by substitution or parts for more complex functions?
5. What happens when you apply integration to rational functions or trigonometric functions?

**Tip:** Always break the integral down term by term for polynomials; it simplifies the process significantly!

Learn how to evaluate the indefinite integral of the polynomial x² - 7x + 2 with respect to x. This step-by-step solution demonstrates polynomial integration and includes the constant of integration. Suitable for students in Grades 10-12.

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