10.1: Double Integrals over Rectangular Regions
( \newcommand{\kernel}{\mathrm{null}\,}\)
- Compute ∫20∫40(1+x) dydx.
- Compute ∫1−1∫2−2(2x+3y+5) dxdy.
- Compute ∫61∫92√yx2 dydx.
- Compute ∫ln3ln2∫10ex+y dydx.
- Compute ∫π0∫π/20sin(2x)cos(3y) dxdy.
- Compute ∫e1∫e1sin(lnx)cos(lny)xy dxdy.
- Compute ∫10∫21xx2+y2 dydx.
- Find the volume under the surface z=xy and over rectangle R=[0,2]×[1,3].
- Find the volume under the surface z=y2 and over rectangle R=[−2,2]×[−1,4].
- Find the volume under the surface z=x√4−x2y and over rectangle R=[0,2]×[1,e].
- Sketch the solid whose volume is expressed as ∬Rx dA, where R=[0,5]×[0,5]. Then use geometry to find the volume.
- Sketch the solid whose volume is expressed as ∬R√4−y2 dA, where R=[0,2]×[0,2]. Then use geometry to find the volume.