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Integration of (1 2x 3x^2 4x^3 .)?
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Integration of (1 2x 3x^2 4x^3 .)?
Integration of (1 + 2x + 3x^2 + 4x^3)
Step 1: Apply the Power Rule
The power rule states that the integral of x^n is (1/(n+1))x^(n+1) + C, where C is the constant of integration. Applying this rule to each term in the integrand, we get:
∫(1 + 2x + 3x^2 + 4x^3) dx = x + x^2 + x^3 + x^4 + C
Step 2: Check Your Answer
To check our answer, we can differentiate it using the power rule:
d/dx (x + x^2 + x^3 + x^4 + C) = 1 + 2x + 3x^2 + 4x^3
As we can see, the derivative of our answer is equal to the original integrand, so we know that our answer is correct.
Step 3: Simplify the Answer
Our answer can be simplified by factoring out an x:
x(1 + x + x^2 + x^3) + C
This is the final answer for the integration of (1 + 2x + 3x^2 + 4x^3).
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Integration of (1 2x 3x^2 4x^3 .)?
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Integration of (1 2x 3x^2 4x^3 .)?
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Integration of (1 2x 3x^2 4x^3 .)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Integration of (1 2x 3x^2 4x^3 .)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integration of (1 2x 3x^2 4x^3 .)?.
Integration of (1 2x 3x^2 4x^3 .)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Integration of (1 2x 3x^2 4x^3 .)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integration of (1 2x 3x^2 4x^3 .)?.
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