Solve each question please.
Integrate the function f over the given region.
f(x,y)=(x)/(6)+(y)/(3) over the trapezoidal region bounded by the x-axis, y-axis, line x=6, and line
y=-(2)/(3)x+7
A) (97)/(3)
B) (160)/(3)
C) (244)/(3)
D) (118)/(3)
Find the volume of the indicated region.
the region that lies under the plane z=4x+2y and over the triangle with vertices at (1,1),(2,1), and (1,2)
A) 4
B) (20)/(3)
C) 8
D) (16)/(3)
Write an equivalent double integral with the order of integration reversed.
int_0^5 int_0^(lnx) 9xdydx
A) int_0^(ln5) int_1^5 9xdxdy
B) int_0^(ln5) int_1^5 45xdxdy
C) int_0^(ln5) int_(e^(5))^5 45xdxdy
D) int_0^(ln5) int_(e^(5))^5 9xdxdy
int_0^8 int_(y^(2))^(64) 3ydxdy
A) int_0^8 int_0^(sqrt(x)) 3ydydx
B) int_0^8 int_8^(sqrt(x)) 3ydydx
C) int_0^(64) int_0^(sqrt(x)) 3ydydx
D) int_0^(64) int_8^(sqrt(x)) 3ydydx
Reverse the order of integration and then evaluate the integral.
int_0^(30) int_((y)/(5))^6 (cosx)/(x)dxdy
A) 5sin6
B) 5cos6
C) 6cos5
12) int_0^9 int_(sqrt((x)/(9)))^1 e^(y^(3))dydx
A) (3)/(2)(2e-1)
B) 3(2e-1)
C) (3)/(2)(e-1)
D) 6sin5
Integrate the function f over the given region
3
T)
2 X+7 3
160 B) 3
C) 244 3
118 D
Find the volume of the indicated region 8) the region that lies under the plane z= 4x +2y and over the triangle with vertices at 1, 1),(2, 1, and1,2 A)4 C) 8
8)
Write an equivalent double integral with the order of integration reversed lnX 9 9x dy dx
9)
9x dx dy
B
45x dx dy
ln5
45x dx dy ey
ln 5
D
9x dx dy
64 3y dx dy
0
10)
VX 3y dy dx
A)
3y dy dx
64
c)
3y dy dx
3y dy dx
Reverse the order of integration and then evaluate the integral. 30 11) cos dx dy X y/5 A)5sin6 B) 5 cos 6 C) 6 cos 5
11)
D) 6 sin 5
12)
x/9
12)
A(2e - 1
B)3(2e-1)
C(e-1
D)3(e-1