Using the Fundamental Theorem of Calculus, what is ∫_0^2 4x dx?

Using the Fundamental Theorem of Calculus, what is ∫_0^2 4x dx?

• A. 6
• B. 8
• C. 4
• D. 12

Answer: (B)

The Fundamental Theorem of Calculus tells us to take an antiderivative of the integrand and evaluate it at the upper limit minus the lower limit. For 4x, an antiderivative is 2x^2. Evaluate from 0 to 2: 2(2)^2 − 2(0)^2 = 8 − 0 = 8. So the integral equals 8. The other numbers would require a different antiderivative or different limits, but with this integrand and bounds, the result is 8.

The Fundamental Theorem of Calculus tells us to take an antiderivative of the integrand and evaluate it at the upper limit minus the lower limit. For 4x, an antiderivative is 2x^2. Evaluate from 0 to 2: 2(2)^2 − 2(0)^2 = 8 − 0 = 8. So the integral equals 8. The other numbers would require a different antiderivative or different limits, but with this integrand and bounds, the result is 8.