Use differentiation to determine whether the integral formula is correct.
-$$\int ( 2 x - 2 ) ^ { 4 } d x = \frac { ( 2 x - 2 ) ^ { 5 } } { 10 } + C$$

Question

Quizplus · Accepted Answer

We can use differentiation to check if the given integral formula is correct or not.

Taking the derivative of the right-hand side of the formula, we get:

\begin{align*}
\frac{d}{dx}\left(\frac{(2x-2)^5}{10}+Cight) &= \frac{1}{10}\cdot \frac{d}{dx}(2x-2)^5 \
&= \frac{1}{10} \cdot 5(2x-2)^4\cdot 2 \
&= (2x-2)^4
\end{align*}

This matches the integrand of the original formula, which is $(2x-2)^4$. Therefore, the given integral formula is correct, and the answer is A.

Use Differentiation to Determine Whether the Integral Formula Is Correct ∫(2x−2)4dx=(2x−2)510+C\int ( 2 x - 2 ) ^ { 4 } d x = \frac { ( 2 x - 2 ) ^ { 5 } } { 10 } + C∫(2x−2)4dx=10(2x−2)5​+C

Use Differentiation to Determine Whether the Integral Formula Is Correct $\int ( 2 x - 2 ) ^ { 4 } d x = \frac { ( 2 x - 2 ) ^ { 5 } } { 10 } + C$