AP problem back ch 7: skip # 7

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Presentation transcript:

AP problem back ch 7: skip # 7 Be seated before the bell rings Agenda : -Review Hw p- 503 ;1-13 odd, 17-21 odd,24 AP problem back ch 7: skip # 7 DESK Warm-up (in your notes) homework

LT3: Find the volume of a non-rotational solid with known cross sections

Area formula Distance S LT3: Find the volume of a non-rotational solid with known cross sections Area formula Distance S

With perpendicular cross section to the x-axis squares Find volume of solid with base bounded by With perpendicular cross section to the x-axis squares

With perpendicular cross section to the x-axis squares Find volume of solid with base bounded by And With perpendicular cross section to the x-axis squares

With perpendicular cross section to the y-axis squares Find volume of solid with base bounded by With perpendicular cross section to the y-axis squares And

With perpendicular cross section to the x-axis rectangle with height 5 Find volume of solid with base bounded by And With perpendicular cross section to the x-axis rectangle with height 5

Find volume of solid with base bounded by And With perpendicular cross section to the x-axis isosceles right triangles . With a leg on the xy plane

Find volume of solid with base bounded by With perpendicular cross section to the x-axis isosceles right triangles . With hypotenuse on xy plane And

More Examples

Find the area of the region bounded by the two curves LT1: Find the area between two curves. Find the area of the region bounded by the two curves

LT1: Find the area between two curves. Sketch the region bounded by the graphs of the equations and find the area of the region

Find the area of the region LT1: Find the area between two curves. Find the area of the region You may use a calculator to evaluate the answer, but be sure to write the integral setup.

Given the area between ,x = 6, and y =0 LT1: Find the area between two curves. Given the area between ,x = 6, and y =0 Find the line x = a such that the area is divided into two equal regions

~20.106 LT2: Find the volume of a rotational solid. Find the volume of the solid created when the region bounded by is rotated around the y axis. ~20.106

LT2: Find the volume of a rotational solid. Find the volume of the solid created when the region bounded by is rotated around the x axis.

LT2: Find the volume of a rotational solid. Find the volume of the solid created when the region bounded by is rotated around the y = 2

LT2: Find the volume of a rotational solid. Find the volume of the solid created when the region bounded by is rotated around the x= 7

is rotated around the x = -1. LT2: Find the volume of a rotational solid. Find the volume of the solid created when the region bounded by is rotated around the x = -1. ~36.861

LT2: Find the volume of a rotational solid.

LT3: Find the volume of a non-rotational solid with known cross sections

LT1: area between two curves Write but do not solve an integral to find the line x = k. that divides the area R in equal halves. OR

LT3: Find the volume of a non-rotational solid with known cross sections

LT3: Find the volume of a non-rotational solid with known cross sections Write but do not evaluate an integral to find the volume of the solid whose base is R if all cross sections perpendicular to the x axis are isosceles right triangles, with a leg as a base

Find the area bounded by the two equation from 0 and 1 LT3: Find the volume of a non-rotational solid with known cross sections Find the area bounded by the two equation from 0 and 1

LT3: Find the volume of a non-rotational solid with known cross sections Write but do not evaluate an integral to find the volume of the solid whose base is R if all cross sections perpendicular to the x axis are semicircles.

LT3: Find the volume of a non-rotational solid with known cross sections Find the volume of the solid created with R as the base if the cross sections perpendicular to the y axis are squares. You may use a calculator to evaluate the answer, but be sure to write the integral setup.

LT 2 Volume of rotational solid About the y – axis

LT 2 Find the volume of the solid revolved about the given axis LT 2 Find the volume of the solid revolved about the given axis. And bounded by the following equation: