[12.2] - Double Integrals - Practice

1. $\int_0^2\int_0^2(x^2-y^2)\,dy\,dx$
   
   
   
   
   
   
2. $\int_0^{\frac{\pi}{4}}\int_{y=0}^{\frac{\pi}{2}}\cos(2x+y)\,dy\,dx$
   Hint: According to one of the Trig addition formulas, $\cos(\alpha+\beta)= \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta)$
   
   
   
   
   
   
3. $\int_0^2\int_{y=1}^3x^3y\,dy\,dx$
   
   
   
   
   
   
4. $\int_{-1}^{1}\int_{y=0}^{\pi}x^2\sin y\,dy\,dx$
   
   
   
   
   
   
5. $\int_0^2\int_{y=x^2}^{2x}(x^2+2y)\,dy\,dx$
   
   
   
   
   
   
6. $\int_0^3\int_{y=0}^{9-x^2}4x\,dy\,dx$
   
   

Answers: 1.) 0     2.) 0     3.) 16     4.) $\frac 43$     5.) $\frac{88}{15}$     6.) 81