{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

272t3as08sol

# 272t3as08sol - Mat 272 Test 3 Dr Firoz A 1 Evaluate the...

This preview shows pages 1–3. Sign up to view the full content.

Mat 272 Test 3 Dr. Firoz 1 A 1. Evaluate the double integral , [0,1] [0,4] x x R e y e dxdy R + = × ∫∫ . Show complete work. Sol: 1 4 0 0 13.3 x x x x R e y e dxdy e y e dxdy + = + = ∫∫ ∫∫ 2. Let R be the region shown in the accompanying figure. Fill in the missing limits of integration. ( , ) ( , ) R f x y dA f x y dydx - - - - = ∫∫ ∫ ∫ y x = R 2 y x = Solution: 2 1 0 ( , ) ( , ) x R x f x y dA f x y dydx = ∫∫ ∫ ∫ 3. Write down the double integral and also triple integral to find the volume of the tetrahedron bounded by the coordinate planes and the plane 4 4 2 z x y = - - . Do not evaluate the integrals. Solution: 1 2 2 0 0 x D zdA z dydx z dydx - - - - - = = ∫∫ ∫ ∫ 4 4 2 1 2 2 0 0 0 x y x V dv dzdydx - - - = ∫∫∫

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Mat 272 Test 3 Dr. Firoz 2 4. Use spherical coordinate to evaluate 2 2 ( ) H x y dv + ∫∫∫ , where H is the hemispherical region that lies above the xy -plane and below the sphere 2 2 2 1 x y z + + = . Solution: 2 / 2 1 2 2 4 3 0 0 0 ( ) sin 4 /15 H x y dv d d d π π ρ φ ρ φ θ π + = = ∫∫∫ ∫ ∫ ∫ B.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

272t3as08sol - Mat 272 Test 3 Dr Firoz A 1 Evaluate the...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online