AP Calculus Volumes and Areas MC

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 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 volume of the solid formed when cross sections perpendicular to the x axis are squares

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Find the volume of the solid formed when cross sections perpendicular to the x axis are semi-circles

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Volume using discs revolving around horizontal line. 

•  $\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$  

•  $\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$  

•  $\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$  

•  $\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$  

Volume using discs revolving around vertical line. 

•  $\pi\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$  

•  $\pi\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$  

•  $\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$  

•  $\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$  

Which of these can you use for calculating area using the Trapezoidal Method?

• $\Delta x\left(\frac{f\left(x_1\right)+f\left(x_2\right)}{2}\right)$

• $\Delta x\left(\frac{f\left(x_1\right)-f\left(x_2\right)}{2}\right)$

• $\Delta x\left(f\left(x_1\right)+f\left(x_2\right)\right)$

• $\Delta x\left(f\left(x_1\right)-f\left(x_2\right)\right)$

If f and g are inverses what is g'(x)?

•  $g'\left(x\right)=\frac{1}{f'\left(g\left(x\right)\right)}$  

•  $g'\left(x\right)=\frac{1}{f'\left(x\right)}$  

•  $g'\left(x\right)=\frac{-1}{f'\left(x\right)}$  

•  $g'\left(x\right)=\frac{-1}{f'\left(g\left(x\right)\right)}$  

 $\int_1^8\left(x^{\frac{1}{3}}+1\right)dx$  

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• 73/4

• -87/4

• 13/4