Question: Find the integral of x^2 with respect to x.
Options:
(1/3)x^3 + C
(1/2)x^3 + C
(1/4)x^4 + C
x^3 + C
Correct Answer: (1/3)x^3 + C
Solution:
The integral of x^2 is (1/3)x^3 + C, where C is the constant of integration.
Find the integral of x^2 with respect to x.
Practice Questions
Q1
Find the integral of x^2 with respect to x.
(1/3)x^3 + C
(1/2)x^3 + C
(1/4)x^4 + C
x^3 + C
Questions & Step-by-Step Solutions
Find the integral of x^2 with respect to x.
Step 1: Identify the function you want to integrate, which is x^2.
Step 2: Use the power rule for integration. The power rule states that the integral of x^n is (1/(n+1)) * x^(n+1) + C, where n is the exponent and C is the constant of integration.
Step 3: In this case, n is 2. So, apply the power rule: (1/(2+1)) * x^(2+1) + C.
Step 4: Simplify the expression: (1/3) * x^3 + C.
Step 5: Write the final answer: The integral of x^2 is (1/3)x^3 + C.
Integration – The process of finding the integral of a function, which represents the area under the curve of that function.
Power Rule for Integration – A rule that states the integral of x^n is (1/(n+1))x^(n+1) + C for any real number n ≠-1.
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