Math Problem Statement

Integrate (2x - 1) dx

Solution

The integral in the image is:

(2x1)dx\int (2x - 1) \, dx

To solve it, we can integrate each term separately:

  1. For the term 2x2x: The integral of 2x2x with respect to xx is 2xdx=x2\int 2x \, dx = x^2.
  2. For the term 1-1: The integral of 1-1 with respect to xx is 1dx=x\int -1 \, dx = -x.

Thus, combining these results:

(2x1)dx=x2x+C\int (2x - 1) \, dx = x^2 - x + C

where CC is the constant of integration.

Final Answer:

x2x+Cx^2 - x + C

Would you like more details on the integration process, or have any questions?


Here are 5 related questions:

  1. How would you integrate (3x4)dx\int (3x - 4) \, dx?
  2. What is the integral of (x23x+5)dx\int (x^2 - 3x + 5) \, dx?
  3. How do you handle integrals involving exponential functions, like e2xdx\int e^{2x} \, dx?
  4. What is the integral of (2x+sinx)dx\int (2x + \sin x) \, dx?
  5. How would you compute a definite integral for 13(2x1)dx\int_{1}^{3} (2x - 1) \, dx?

Tip: When integrating, separate terms if possible to make integration easier term by term.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Integration
Calculus
Polynomial Functions

Formulas

∫ (ax + b) dx = (a/2)x^2 + bx + C

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 10-12