Definite integrals and area under a curve Quiz

1. Evaluate $\int_1^3(2x+1)\,\mathrm{d}x$.

• A. $10$
• B. $8$
• C. $12$
• D. $6$

2. Evaluate $\int_0^2\left(x^2-2x\right)\mathrm{d}x$.

• A. $\frac43$
• B. $-\frac43$
• C. $\frac83$
• D. $0$

3. Find the area between $y=x$ and $y=x^2$ for $0\le x\le1$.

• A. $\frac13$
• B. $\frac12$
• C. $\frac16$
• D. $\frac56$

4. Given $\int_1^4f(x)\,\mathrm{d}x=7$, find $\int_4^1f(x)\,\mathrm{d}x$.

• A. $7$
• B. $\frac17$
• C. $-\frac17$
• D. $-7$

5. Find the total area between $y=x^3$ and the $x$-axis for $-1\le x\le1$.

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