Area and Volume (Calculus)

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.

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

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

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

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

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.CED.A.2

CCSS.HSA.APR.A.1

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

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

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

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

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

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.C.7

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

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

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

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

•  $\pi\int_a^b\ \ R\ dx$  

Tags

CCSS.HSG.GMD.A.3

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

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

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

• $\pi\int_a^b\left[R^2-r^2\right]dx$

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

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

If the region from (-1,0) is rotated about the x axis, would one use a washer or disk?

• washer
• disk

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

If the region enclosed by these functions are revolved around the y axis, would one use a washer or disk?

• washer
• disk

Tags

CCSS.HSG.GMD.A.3

CCSS.HSG.GMD.A.1

What is the outer radius (R) needed to find the volume of the region revolving around  $y=1$  ?

•  $1-\left(-x^2+6\right)$  

•  $\left(-x^2+6\right)-1$  

•  $2-1$  

•  $1-2$  

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Select the integral that would find the volume of the region revolving around the given axis.

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Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Select the integral that would find the volume of the region revolving around the given axis.

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Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9