3. ∫(6t² - 4t + 3) dt
3. ∫(6t² - 4t + 3) dt
Answer
Explanation:
Step1: Apply integral sum - difference rule
$\int(6t^{2}-4t + 3)dt=\int6t^{2}dt-\int4tdt+\int3dt$
Step2: Use power - rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C(n\neq - 1)$
For $\int6t^{2}dt$, we have $6\times\frac{t^{2 + 1}}{2+1}=2t^{3}$; for $\int4tdt$, we have $4\times\frac{t^{1+1}}{1 + 1}=2t^{2}$; for $\int3dt$, we have $3t$.
Step3: Combine the results
$2t^{3}-2t^{2}+3t + C$
Answer:
$2t^{3}-2t^{2}+3t + C$