evaluate the definite integral below. ∫₁⁵ -3x² dx

Explanation:

Step1: Find antiderivative

The antiderivative of $-3x^{2}$ is $-3\times\frac{x^{3}}{3}=-x^{3}$ using the power - rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$).

Step2: Apply fundamental theorem of calculus

$\int_{1}^{5}-3x^{2}dx=\left[-x^{3}\right]_{1}^{5}=-(5^{3})-(-(1^{3}))$.

Step3: Calculate the result

$-(5^{3})-(-(1^{3}))=-125 + 1=-124$.

Answer:

$-124$