Area between a curve and a line or two curves Quiz

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

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

2. The curve $y=x^2$ meets the line $y=6-x$ at $x=-3$ and $x=2$. Which integrand gives the area between them?

• A. $x^2-6+x$
• B. $6-x+x^2$
• C. $6-x-x^2$
• D. $x^2-x$

3. Find the $x$-coordinates of the points where $y=x^2$ meets $y=3x+4$.

• A. $x=1$ and $x=-4$
• B. $x=3$ and $x=4$
• C. $x=-3$ and $x=-4$
• D. $x=-1$ and $x=4$

4. Find the area between $y=9-x^2$ and $y=x^2-9$.

• A. $36$
• B. $72$
• C. $18$
• D. $144$

5. The area under $y=x+2$ from $x=-1$ to $2$ is $\frac{15}{2}$ and the area under $y=x^2$ over the same interval is $3$. The area between them is

• A. $3$
• B. $\frac{15}{2}$
• C. $\frac92$
• D. $\frac{21}{2}$