5.11 Definite integrals and areas Quiz

1. Find $\int_0^3 (2x + 1)\,\mathrm{d}x$.

• A. $7$
• B. $12$
• C. $9$
• D. $6$

2. Find $\int_0^{\pi} \sin x\,\mathrm{d}x$.

• A. $0$
• B. $1$
• C. $-2$
• D. $2$

3. The curve $y = x^2 - 1$ is below the $x$-axis for $-1 < x < 1$. Find the area enclosed by the curve and the $x$-axis.

• A. $-\frac{4}{3}$
• B. $\frac{4}{3}$
• C. $\frac{2}{3}$
• D. $0$

4. Given $\int_1^4 f(x)\,\mathrm{d}x = 6$, find $\int_1^4 (2f(x) - 1)\,\mathrm{d}x$.

• A. $11$
• B. $9$
• C. $12$
• D. $8$

5. The curves $y = 4 - x^2$ and $y = 0$ enclose a region. Which integral gives its area?

• A. $\int_0^4 (4 - x^2)\,\mathrm{d}x$
• B. $\int_{-2}^{2} (x^2 - 4)\,\mathrm{d}x$
• C. $\int_{-2}^{2} (4 - x^2)\,\mathrm{d}x$
• D. $\int_{-4}^{4} (4 - x^2)\,\mathrm{d}x$