Class 12 Exam > Class 12 Questions > Integrate 3x2(cosx3+8).a)sinx3−8x3+Cb)s...
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Integrate 3x2(cosx3+8).
- a)sinx3−8x3+C
- b)sinx3+8x3+C
- c)–sinx3+8x3+C
- d)sinx3−x3+C
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Integrate 3x2(cosx3+8).a)sinx3−8x3+Cb)sinx3+8x3+Cc)–sinx3+...
By using the method of integration by substitution,
Let x3=t
Differentiating w.r.t x, we get
3x2 dx=dt
∫3x2(cosx3+8)dx=∫(cost+8)dt
∫(cost+8)dt=sint+8t
Replacing t with x3,we get
∫3x2(cosx3+8)dx=sinx3+8x3+C
Let x3=t
Differentiating w.r.t x, we get
3x2 dx=dt
∫3x2(cosx3+8)dx=∫(cost+8)dt
∫(cost+8)dt=sint+8t
Replacing t with x3,we get
∫3x2(cosx3+8)dx=sinx3+8x3+C
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Integrate 3x2(cosx3+8).a)sinx3−8x3+Cb)sinx3+8x3+Cc)–sinx3+...
To integrate 3x^2(cos(x^3 + 8)), we can use u-substitution. Let u = x^3 + 8, then du = 3x^2 dx.
Now the integral becomes ∫cos(u) du.
Integrating cos(u), we get sin(u) + C, where C is the constant of integration.
Substituting back x^3 + 8 for u, we have ∫cos(x^3 + 8) dx = sin(x^3 + 8) + C.
So the answer is sin(x^3 + 8) + C.
Now the integral becomes ∫cos(u) du.
Integrating cos(u), we get sin(u) + C, where C is the constant of integration.
Substituting back x^3 + 8 for u, we have ∫cos(x^3 + 8) dx = sin(x^3 + 8) + C.
So the answer is sin(x^3 + 8) + C.
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Integrate 3x2(cosx3+8).a)sinx3−8x3+Cb)sinx3+8x3+Cc)–sinx3+8x3+Cd)sinx3−x3+CCorrect answer is option 'B'. Can you explain this answer?
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