Definite Integrals and Area

Find ∫ from $0$ to $3$ of $x^2$ dx.

• 1Find an antiderivative: F($x$) = $\frac{x^3}{3}$
• 2Evaluate at the top limit: F($3$) = $\frac{3^3}{3}=\frac{27}{3}=9$
• 3Evaluate at the bottom limit: F($0$) = $\frac{0^3}{3}=0$
• 4Subtract: F($3$) − F($0$) = $9-0$

Answer: $9$

Find ∫ from $1$ to $4$ of $2x$ dx.

• 1Find an antiderivative: F($x$) = $x^2$
• 2Evaluate: F($4$) = $16$, F($1$) = $1$
• 3Subtract: $16-1$

Answer: $15$