Find the indefinite integral and check the result by differentiation. $\int ( - 8 t + 3 ) d t$
A) $- 4 t ^ { 2 } + 3 t + C$
B) $- 8 t ^ { 2 } + 3 t + C$
C) $- 4 t ^ { 2 } + 3 t$
D) $- 8$
E)none of the above

Question

Quizplus · Accepted Answer

The integral of $-8t + 3$ with respect to $t$ is $-4t^2 + 3t + C$, where $C$ is the constant of integration. This is because the antiderivative of $-8t$ is $-4t^2$ (using the power rule for integration, $\int t^n dt = \frac{t^{n+1}}{n+1} + C$ for $n \neq -1$), and the antiderivative of $3$ is $3t$, since integrating a constant $a$ gives $at + C$.

Find the Indefinite Integral and Check the Result by Differentiation ∫(−8t+3)dt\int ( - 8 t + 3 ) d t∫(−8t+3)dt

Find the Indefinite Integral and Check the Result by Differentiation $\int ( - 8 t + 3 ) d t$