Evaluate $\displaystyle\int_0^2 x^2\,dx$.

**Finding the antiderivative** $$F(x)=\int x^2\,dx=\frac{x^3}{3}$$ **Applying the Fundamental Theorem** $$\int_0^2x^2\,dx=F(2)-F(0)=\frac{2^3}{3}-\frac{0^3}{3}=\frac83-0=\frac83$$ …

Evaluate ∫₀² x²dx.

Worked Examples · Example 6

\displaystyle\int_0^2 x^2\,dx

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Concept understanding — Definite Integral (Fundamental Theorem and Properties)

$\int_a^b f(x)\,dx=F(b)-F(a)$ gives the definite integral as a number, with no arbitrary constant; standard properties (reversing limits, splitting the interval, substituting $a+b-x$ ) simplify e …

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Q.Evaluate ∫02x2 dx\displaystyle\int_0^2 x^2\,dx∫02​x2dx.

Concept understanding — Definite Integral (Fundamental Theorem and Properties)

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Q.Evaluate $\displaystyle\int_0^2 x^2\,dx$ .

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