CALC 2 CHAPTER 6 EXAM QUESTIONS AND ANSWERS -20

CALC 2 CHAPTER 6 EXAM QUESTIONS AND
ANSWERS #20
Find the area of the Region
Y = sin(x), y = 3x, x = π/2, x = π - correct answer ((9π^2)/8)-1

Find the area of the shaded region.
X=y^2-8, x=e^y, y=1, y=-1 - correct answer e-1/e-46/3

Find the area of the shaded region.
X = 63 − 7y^2, x = 7y^2 − 63 - correct answer 504

Find its Area
Y = 3/x, y = 12x, y = 1/3x, x > 0 - correct answer 3ln(6)

Find it's area
Y = |7x|, y = x^2 − 8 - correct answer 704/3

Find the area of the region bounded by the curves
Y = sin(x),
Y = cos(x),
X = 0,
And
X = π/2. - correct answer 2√2 -2

Find the volume V of the solid obtained by rotating the region bounded by the given
curves about the specified line.
Y = x + 1, y = 0, x = 0, x = 7; about the x-axis - correct answer 511π/3

Find the volume V of the solid obtained by rotating the region bounded by the given
curves about the specified line.
2x = y^2, x = 0, y = 5;
About the y-axis - correct answer 625π/4

Find the volume V of the solid obtained by rotating the region bounded by the given
curves about the specified line.
Y = 27x^3, y = 0, x = 1; about x = 2 - correct answer 81π/4

The integral represents the volume of a solid. Describe the solid.
Π∫(y6 − y16) dy, a=0 and b=1 - correct answer ℛ = (x, y) | 0 ≤ y ≤ 1, y^8 ≤ x ≤ y^3

Find the volume V of the solid obtained by rotating the region bounded by the given
curves about the specified line.
Y = 1/25x^2, x = 5, y = 0; about the y-axis - correct answer (25/2)π