Question

Evaluate the integral \[ \int_0^2 x^2 + 2x - 3 \, dx \]

• A. 3
• B. 6
• C. 2
• D. 4

Hint:

When solving definite integrals, always ensure you properly evaluate the antiderivative at the upper and lower limits of integration.

Answer 1

The Correct Option is D

To solve this definite integral, we first find the antiderivative of the function \(x^2 + 2x - 3\). The antiderivative is \(\frac{x^3}{3} + x^2 - 3x\). Evaluating this from 0 to 2 gives: \[ \left(\frac{2^3}{3} + 2^2 - 3(B)\right) - \left(\frac{0^3}{3} + 0^2 - 3(0)\right) = \left(\frac{8}{3} + 4 - 6\right) - (0) = \frac{8}{3} + (-2) = 4 \] Thus, the value of the integral is 4.