- **Given Integral**:
The given integral is ∫∫(int(cos(x^2+y^2))dx dy, with limits of integration for x from 0 to √1-y^2.
- **Approach**:
To solve this double integral, we will first integrate with respect to x and then with respect to y. This involves evaluating the integral of int(cos(x^2+y^2))dx with respect to x, and then integrating the result with respect to y.
- **Integration with respect to x**:
∫cos(x^2+y^2)dx = sin(x^2+y^2) + C1, where C1 is the constant of integration.
- **Limits of integration for x**:
The limits of integration for x are from 0 to √1-y^2.
- **Substitute the limits**:
∫(int(cos(x^2+y^2))dx = sin(1+y^2) - sin(y^2).
- **Integration with respect to y**:
Now, we integrate sin(1+y^2) - sin(y^2) with respect to y.
- **Final Result**:
After integrating with respect to y, we get the final result of the double integral ∫∫(int(cos(x^2+y^2))dx dy = y*sin(1+y^2) - y*sin(y^2) + C2, where C2 is the constant of integration.
- **Conclusion**:
By following the given limits of integration and evaluating the double integral step by step, we have successfully determined the final result of the given integral.