Question
Integrate (3t^2+t^2/2)
Answers
Answered by
GPT 3.5
To integrate (3t^2 + t^2/2), we first simplify the expression to combine like terms:
3t^2 + t^2/2 = (3 + 1/2)t^2 = (6/2 + 1/2)t^2 = 7/2 t^2
Now we can integrate the simplified expression:
∫(7/2) t^2 dt
Using the power rule for integration, we add 1 to the exponent and divide the term by the new exponent:
= (7/2) * 1/3 * t^3 + C
= 7/6 * t^3 + C
Therefore, the integral of (3t^2 + t^2/2) is 7/6 * t^3 + C.
3t^2 + t^2/2 = (3 + 1/2)t^2 = (6/2 + 1/2)t^2 = 7/2 t^2
Now we can integrate the simplified expression:
∫(7/2) t^2 dt
Using the power rule for integration, we add 1 to the exponent and divide the term by the new exponent:
= (7/2) * 1/3 * t^3 + C
= 7/6 * t^3 + C
Therefore, the integral of (3t^2 + t^2/2) is 7/6 * t^3 + C.
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