Find the value of the definite integral ∫_0^3 (2x-1),dx.

Find the value of the definite integral $\int_{0}^{3} (2 x - 1), d x$ .

easy 1 mark Class 12 · Mathematics · Integrals

Answer

The correct answer is 6 — Therefore the value of the integral is $6$ .

Set up the integral: $\int_{0}^{3} (2 x - 1), d x$ .
Find the antiderivative: $\int (2 x - 1), d x = x^{2} - x + C$ .
Evaluate the antiderivative at the limits: $[x^{2} - x]_{0}^{3} = (9 - 3) - (0 - 0) = 6$ .
Therefore the value of the integral is $6$ .

Common mistake: Forgetting to apply the limits of integration correctly

Concept tested: Definite integral of a polynomial