Use the given transformation to evaluate the integral. (12x +
8y) dA R , where R...
Use the given transformation to evaluate the integral. (12x +
8y) dA R , where R is the parallelogram with vertices (−1, 3), (1,
−3), (2, −2), and (0, 4) ; x = 1/ 4 (u + v), y = 1/ 4 (v − 3u)
using / for integral
Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is
the trapezoidal region with vertices (1,0), (2,0), (0,2), and
(0,1)
1.) Evaluate the given definite integral.
Integral from 4 to 5 dA∫45 (0.2e^−0.2A +3/A) dA
2.) Evaluate the definite integral.
Integral from negative 1 to 1 dx∫−1 1 (x^2+1) dx
3.) Evaluate the definite integral.
Integral from 0 to 2 dx∫02 (2x^2+x+6) dx
4.) Evaluate the definite integral.
Integral from 1 to 4 left dx∫14 (x^3/2+x^1/2−x^−1/2) dx
5.) Evaluate the definite integral.
Integral from negative 2 to negative 1 dx∫−2−1 (3x^−4) dx
evaluate the integral by making an appropriate change of
variables
double integral of 5sin(25x^2+64y^2) dA, where R is the region
in the first quadrant bounded by the ellipse 25x^2 +64y^2=1
1) Evaluate the double integral ∬Dx^2 y dA, where D is the top
half of the disc with center the origin and radius 2 by changing to
polar coordinates.
2) Use a double integral to find the area of one loop of the
rose r= 6cos (3θ).
3) Use polar coordinates to find the volume of the solid below
the paraboloid z=50−2x^2−2y^2 and above the xy-plane.
1. Evaluate the double integral for the function
f(x,y) and the given region
R.
R is the rectangle defined by
-2 x 3 and
1 y e4
2. Evaluate the double integral
f(x, y) dA
R
for the function f(x, y) and the
region R.
f(x, y) =
y
x3 + 9
; R is bounded by the lines
x = 1, y = 0, and y = x.
3. Find the average value of the function
f(x,y) over the plane region
R....
Evaluate the line integral, where C is the given curve, where C
consists of line segments from (1, 2, 0) to (-3, 10, 2) and from
(-3, 10, 2) to (1, 0, 1).
C zx dx + x(y − 2) dy
Evaluate the line integral
C
F · dr,
where C is given by the vector function
r(t).
F(x, y, z) = sin(x) i + cos(y) j + xz k
r(t) = t5 i − t4 j + t k, 0 ≤ t ≤ 1