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evaluate ∫ ∫ R f(x,y) dy dx over the region

0 votes

evaluate ∫  R  f(x,y) dy dx over the region

1. R= {(x,y)| 0 ≤ x ≤ 1 and 0 ≤ y ≤ x} where f(x,y)= 24y^2e^(x^4+1)

2. R={(x,y)| 0 ≤  x ≤  y and 0 ≤  y ≤  2 } where f(x,y) = 12e^(4y+2)

3. Find the volume of the solid under the graph of the function f(x,y) = 18x^2y^2 and over the region R= {(x,y)| 0 ≤ x ≤ 1 and -1 ≤  y ≤  2 }

asked Nov 8, 2015 in CALCULUS by anonymous

3 Answers

0 votes

Fubini's Theorem:

If image is continuous on the rectangle image then image.

(1)

image and image.

Evaluate image.

image

image

image

image

answered Nov 9, 2015 by Lucy Mentor
0 votes

Fubini's Theorem:

If image is continuous on the rectangle image then image.

(2)

image and image.

Evaluate image.

image

image

Apply integration by parts.

Integration by parts: image.

Consider image then image.

Consider image then image.

image

image

answered Nov 9, 2015 by Lucy Mentor
edited Nov 9, 2015 by Lucy
0 votes

(3)

Find the volume of the solid.

image and image.

Evaluate image.

image

image

answered Nov 9, 2015 by Lucy Mentor
edited Nov 9, 2015 by Lucy

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