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: Find the antiderivative of x^3. We use the power rule for integration, which states that x^n \,dx = x^n+1n+1. Here, n=3. x^3 \,dx = x^3+13+1 = (x^4)/(4) Step 2: Evaluate the definite integral using the limits of integration. The definite integral is evaluated as F(b) - F(a), where F(x) is the antiderivative and a and b are the lower and upper limits, respectively. _2^4 x^3 \,dx = [ (x^4)/(4) ]_2^4 Step 3: Substitute the upper limit (x=4) and the lower limit (x=2) into the antiderivative. (4^4)/(4) - (2^4)/(4) Step 4: Calculate the values. (256)/(4) - (16)/(4) 64 - 4 60 The final answer is 60. Send me the next one 📸