RL Calculus - Area and Volume

Select the formula for finding area under a curve bounded by the x axis.

•  $\int_a^bf\left(x\right)dx$  

•  $\int_a^b\left[f\left(x\right)-g\left(x\right)\right]\ dx$  

•  $\int_a^b\left[f\left(x\right)\right]^2dx$  

•  $\pi\int_a^bf\left(x\right)dx$  

Find the integral for the area under the curve.

• $\int_{-6}^{-2}\ 2\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

• $\int_{-6}^{-2}\ -2\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

• $\int_{-6}^{-2}\ \left(x^2\ +\ 6x\ +\ 10\right)\ dx$

• $\int_{-6}^{-2}\ -4\left(x^2\ +\ 6x\ +\ 10\right)\ dx$

Find the area under the curve over the given interval.

• $\frac{4}{3}$

• $1$

• $\frac{3}{2}$

• $\sqrt{3}$

Select the formula to find the area of ar region between two curves.

• $\int_a^bf\left(x\right)dx$

• $\int_a^bf\left(x\right)^2dx$

• $\int_a^b\left[f\left(x\right)-g\left(x\right)\right]dx$

• $\int_a^b\left[f\left(x\right)^2-g\left(x\right)^2\right]dx$

Find the integral that would find the area of the region enclosed by the curves.

• $\int_0^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx$

• $\int_1^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx$

• $\int_1^5\left[\left(-\frac{x^2}{2}+4x-3\right)-\left(-x^2+6x-8\right)\right]dx$

• $\int_0^5\left[\left(-x^2+6x-8\right)-\left(-\frac{x^2}{2}+4x-3\right)\right]dx$

Find the area of the region enclosed by the curves.

• $\frac{16}{3}$

• $\frac{17}{3}$

• $\frac{13}{3}$

• $\frac{32}{3}$

Select the formula(s) for find the volume of a solid of revolution around an axis using the disk method.

•  $\pi\int_a^b\ f\left(x\right)^2\ dx$  

•  $\pi\int_a^b\ f\left(y\right)^2\ dy$  

•  $\pi\int_a^b\ f\left(x\right)^{ }dx$  

•  $\pi\int_a^b\ \ R\ dx$  

Select the formula(s) to find the volume of a solid of revolution using the washer method.

• $\pi\int_a^b\left[f\left(x\right)-g\left(x\right)\right]dx$

• $\pi\int_a^b\left[f\left(x\right)^2-g\left(x\right)^2\right]dx$

• $\pi\int_a^b\left[R^2-r^2\right]dx$

•  $\pi\int_a^b\left[f\left(y\right)^2-g\left(y\right)^2\right]dy$ 

If the region bounded by the function and the x axis is rotated about the line y = 3, would one use the washer or disk method? 

• washer
• disk

If the same region of the same graph is now rotated about the line y= -4, would one use a washer or disk?

• washer
• disk