This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
Hey @midnight_puff, good to see you again. Step 1: Find the antiderivative of the function. We use the power rule for integration, x^n \,dx = x^n+1n+1. (3x^2 - 4x + 5) \,dx = 3x^2+12+1 - 4x^1+11+1 + 5x + C = 3(x^3)/(3) - 4(x^2)/(2) + 5x + C = x^3 - 2x^2 + 5x + C For definite integrals, we don't need the constant C. So, the antiderivative is F(x) = x^3 - 2x^2 + 5x. Step 2: Apply the Fundamental Theorem of Calculus. The definite integral is evaluated as F(b) - F(a), where b=3 and a=2. _2^3 (3x^2 - 4x + 5) \,dx = [x^3 - 2x^2 + 5x]_2^3 Step 3: Substitute the upper limit (x=3) into the antiderivative. F(3) = (3)^3 - 2(3)^2 + 5(3) = 27 - 2(9) + 15 = 27 - 18 + 15 = 9 + 15 = 24 Step 4: Substitute the lower limit (x=2) into the antiderivative. F(2) = (2)^3 - 2(2)^2 + 5(2) = 8 - 2(4) + 10 = 8 - 8 + 10 = 0 + 10 = 10 Step 5: Subtract the value at the lower limit from the value at the upper limit. F(3) - F(2) = 24 - 10 = 14 The final answer is 14. Send me the next one 📸