question find ∫₁³ (18x - 4)dx
question find ∫₁³ (18x - 4)dx
Answer
Answer:
76
Explanation:
Step1: Find antiderivative
The antiderivative of $18x - 4$ is $9x^{2}-4x+C$. Here we can ignore $C$ for definite - integral.
Step2: Apply fundamental theorem of calculus
[ \begin{align*} \int_{1}^{3}(18x - 4)dx&=(9x^{2}-4x)\big|_{1}^{3}\ &=(9\times3^{2}-4\times3)-(9\times1^{2}-4\times1)\ &=(9\times9 - 12)-(9 - 4)\ &=(81-12)-(9 - 4)\ &=69 - 5\ &=76 \end{align*} ]