Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Integral property:
- ∫ xn dx =
+ C ; n ≠ -1 + C - ∫ ex dx = ex+ C
- ∫ ax dx = (ax/ln a) + C ; a > 0, a ≠ 1
- ∫ sin x dx = - cos x + C
- ∫ cos x dx = sin x + C
Substitution method: If the function cannot be integrated directly substitution method is used. To integration by substitution is used in the following steps:
- A new variable is to be chosen, say “t”
- The value of dt is to be determined.
- Substitution is done and the integral function is then integrated.
- Finally, the initial variable t, to be returned.
Calculation:
I =
Let 3x2 = t; ⇒ 6x dx = dt
I =
I =
I =
Putting up the limits
I =
I =
I =
I =
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