Definite integrals and area under a curve Quiz

1. Evaluate $\int_0^2 3x^2\,dx$.

• A. $12$
• B. $6$
• C. $4$
• D. $8$

2. Evaluate $\int_1^4 x^{-\frac12}\,dx$.

• A. $2$
• B. $1$
• C. $3$
• D. $6$

3. Find the area under $y=x^2$ between $x=1$ and $x=3$.

• A. $8$
• B. $\frac{28}{3}$
• C. $\frac{26}{3}$
• D. $9$

4. Evaluate $\int_2^0(x+1)\,dx$.

• A. $4$
• B. $-4$
• C. $0$
• D. $2$

5. The integral $\int_{-1}^1x^3\,dx$ is $0$. What is the total area between $y=x^3$ and the $x$-axis for $-1\leq x\leq1$?

• A. $0$
• B. $\frac14$
• C. $1$
• D. $\frac12$