MAT 302 Assignment Problem 7.1

MAT 302 Assignment Problem 7.1 | Borough of Manhattan Community College

7.1 Area of Region Between Two Curves

Question 1

(1 point)
Find the area of the region that is enclosed between y=11x2−x3+xy=11x2−x3+x and y=x2+25xy=x2+25x.

Question 2

1 point) Find the area of the region enclosed by the two functions y=5x2y=5x2 and y=x2+4.y=x2+4.

Question 3

(1 point)

Find the area of the region between the curves y=12−x2y=12−x2 and y=x2−6.

Question 4

(1 point)

Find the area of the region between the curves y=xy=x and y=x√3.

Question 5

(1 point) Find the area of the region that is enclosed between y=12x2−x3+xy=12x2−x3+x and y=x2+29xy=x2+29x.

Question 6

(1 point) Sketch the region bounded by the graphs of the functions and find the area of the region.

f(x)f(x) = sin(x)sin(x),   g(x)g(x) = cos(2x)cos(2x), −π2≤x≤π6

Question 7

(1 point) Sketch the region bounded by the graphs of the functions and find the area of the region.

f(x)=xe−x2f(x)=xe−x2,   y=0y=0, 1≤x≤3

Question 8

The boundaries of the shaded region are the yy-axis, the line y=1y=1, and the curve y=x√4.y=x4. Find the area of this region by writing xx as a function of yy and integrating with respect to yy.

Question 9

(1 point)

The area of the region that lies to the right of the yy-axis and to the left of the parabola x=2y−y2x=2y−y2 (the shaded region in the figure) is given by the integral ∫20(2y−y2)dy.∫02(2y−y2)dy. (Turn your head clockwise and think of the region as lying below the curve x=2y−y2x=2y−y2 from y=0y=0 to y=2y=2.) Find the area of the region.

Question 10

(1 point)

Find the area of the shaded region below.

Question 11

 (1 point) Sketch the region enclosed by the curves given below. Decide whether to integrate with respect to xx or yy. Then find the area of the region.

x=64−y2,x=y2−64

Question 12

(1 point) Sketch the region enclosed by 2y=4x√,y=5,2y=4x,y=5, and 2y+2x=62y+2x=6.

Decide whether to integrate with respect to xx or yy, and then find the area of the region.

Question 13

(1 point)

Find the area of the region between the curves 4x+y2=124x+y2=12 and x=y.