This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Write the given definite integral. _x=1^x=2 (x^2 - (1)/(x)) dx Step 2: Find the antiderivative of each term in the integrand. The antiderivative of x^2 is x^2+12+1 = (x^3)/(3). The antiderivative of (1)/(x) is |x|. So, the antiderivative of (x^2 - (1)/(x)) is (x^3)/(3) - |x|. Step 3: Evaluate the definite integral using the Fundamental Theorem of Calculus. [(x^3)/(3) - |x|]_1^2 Substitute the upper limit (x=2) and subtract the result of substituting the lower limit (x=1). ((2^3)/(3) - |2|) - ((1^3)/(3) - |1|) Step 4: Simplify the expression. ((8)/(3) - 2) - ((1)/(3) - 0) Since 1 = 0. (8)/(3) - 2 - (1)/(3) Combine the fractional terms. ((8)/(3) - (1)/(3)) - 2 (7)/(3) - 2 The final answer is: (7)/(3) - 2 That's 2 down. 3 left today — send the next one.