question find ∫₂⁵(8x - 5)dx

Explanation:

Step1: Find antiderivative

The antiderivative of (8x - 5) is (8\times\frac{x^{2}}{2}-5x=4x^{2}-5x) using the power - rule (\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C) ((n\neq - 1)).

Step2: Apply the fundamental theorem of calculus

(\int_{2}^{5}(8x - 5)dx=(4x^{2}-5x)\big|_{2}^{5}=(4\times5^{2}-5\times5)-(4\times2^{2}-5\times2)) First, calculate (4\times5^{2}-5\times5): (4\times25-25 = 100 - 25=75) Then, calculate (4\times2^{2}-5\times2): (4\times4 - 10=16 - 10 = 6) Finally, (75-6 = 69)

Answer:

69