question find ∫₂³ (-16x + 2)dx
question find ∫₂³ (-16x + 2)dx
Answer
Explanation:
Step1: Find antiderivative
The antiderivative of $- 16x+2$ is $-16\times\frac{x^{2}}{2}+2x=-8x^{2}+2x$.
Step2: Apply fundamental theorem of calculus
[ \begin{align*} &\left(-8x^{2}+2x\right)\big|_{2}^{3}\ =&(-8\times3^{2}+2\times3)-(-8\times2^{2}+2\times2)\ =&(-8\times9 + 6)-(-8\times4+4)\ =&(-72 + 6)-(-32 + 4)\ =&-66-(-28)\ =&-66 + 28\ =&-38 \end{align*} ]
Answer:
$-38$