Class 12 Exam > Class 12 Questions > Find the integral of 8x3+1.a)2x4+x+Cb)2x6-5x+...
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Find the integral of 8x3+1.
- a)2x4+x+C
- b)2x6-5x+C
- c)2x4-x+C
- d)2x4+x2 C
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Find the integral of 8x3+1.a)2x4+x+Cb)2x6-5x+Cc)2x4-x+Cd)2x4+x2 CCorre...
∫8x3+1dx
Using
∫8x3+1dx=∫8x3dx+∫1dx
=2x4+x+C.
Using
∫8x3+1dx=∫8x3dx+∫1dx
=2x4+x+C.
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Community Answer
Find the integral of 8x3+1.a)2x4+x+Cb)2x6-5x+Cc)2x4-x+Cd)2x4+x2 CCorre...
Understanding the Integral
To solve the integral of the function 8x^3 + 1, we need to apply the power rule of integration. The power rule states that the integral of x^n is (x^(n+1))/(n+1) + C, where C is the constant of integration.
Step-by-step Integration
- Identify the Terms:
- The function consists of two terms: 8x^3 and 1.
- Integrate Each Term:
- For the term 8x^3:
- Apply the power rule:
- Integral of 8x^3 = 8 * (x^(3+1))/(3+1) = 8 * (x^4)/4 = 2x^4.
- For the constant term 1:
- The integral of 1 is simply x.
- Combine the Results:
- Combining both results gives:
- Integral of (8x^3 + 1) = 2x^4 + x + C.
Conclusion
Thus, the correct answer for the integral of 8x^3 + 1 is:
- Option A: 2x^4 + x + C.
This matches our derived result, confirming that option A is indeed the correct answer.
To solve the integral of the function 8x^3 + 1, we need to apply the power rule of integration. The power rule states that the integral of x^n is (x^(n+1))/(n+1) + C, where C is the constant of integration.
Step-by-step Integration
- Identify the Terms:
- The function consists of two terms: 8x^3 and 1.
- Integrate Each Term:
- For the term 8x^3:
- Apply the power rule:
- Integral of 8x^3 = 8 * (x^(3+1))/(3+1) = 8 * (x^4)/4 = 2x^4.
- For the constant term 1:
- The integral of 1 is simply x.
- Combine the Results:
- Combining both results gives:
- Integral of (8x^3 + 1) = 2x^4 + x + C.
Conclusion
Thus, the correct answer for the integral of 8x^3 + 1 is:
- Option A: 2x^4 + x + C.
This matches our derived result, confirming that option A is indeed the correct answer.
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Find the integral of 8x3+1.a)2x4+x+Cb)2x6-5x+Cc)2x4-x+Cd)2x4+x2 CCorrect answer is option 'A'. Can you explain this answer?
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