What is the integral of f(x) = 2x with respect to x?
Practice Questions
1 question
Q1
What is the integral of f(x) = 2x with respect to x?
x^2 + C
2x^2 + C
x^2 + 2C
2x + C
The integral ∫2x dx = x^2 + C.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the integral of f(x) = 2x with respect to x?
Solution: The integral ∫2x dx = x^2 + C.
Steps: 7
Step 1: Identify the function you want to integrate, which is f(x) = 2x.
Step 2: Recall the basic rule of integration for power functions: ∫x^n dx = (x^(n+1))/(n+1) + C, where n is a constant and C is the constant of integration.
Step 3: In our case, we can rewrite 2x as 2 * x^1. Here, n = 1.
Step 4: Apply the integration rule: Increase the exponent by 1 (1 + 1 = 2) and divide by the new exponent (2).
Step 5: Multiply by the constant 2: (2 * x^2) / 2 = x^2.
Step 6: Don't forget to add the constant of integration, C, to the result.
Step 7: Combine everything to get the final answer: ∫2x dx = x^2 + C.
