Course Code mth381 Question The line y=2x and the parabola \(y^2=16x\) intersect at x=4. Find by a double integral, the area enclosed by\( y=2x\),\(y^{2}=16x\) and the ordinate at\( x=1\) and the point of intersection at\( x=4\) Answer 3.67 Question Evaluate \(I=\int\int\int_{V}3\left(x^{2}+y^2{2}+z^{3}\right)dV\) by changing to polar coordinate Answer \(4\frac{4}{5}a^{5}\pi\) Question Find the volume of the sold bounded by the planes z=0,x=1,x=2,y=-1,y=1 and the surface \(z=x^{2}+y^{2}\) Answer \(V=5\frac{1}{3}\)units Question Evaluate \(\int_{1}^{2} \int_{0}^{\pi}(3+\sin\theta)d\theta dr\) Answer \(3\pi+2\) Question Determine the Jacobian of the functions \(x = r \cos\theta \)and \(y= r\sin\theta\) Answer \(r\) Question Find the integral \(\int_{0}^{\pi}\int_{0}^{\frac {\pi}{2}}\int_{0}^{r} x^{2}\sin\theta dx d\theta d\phi \) Answer \(\frac{\pi r}{2}\) Question Evaluate the \(\int_{0}^{2} dx\int_{1}^{3} dy \int_{1}^{2} xy^{2}z dz\) Answer 26 Question Determine the integral \(I=\int_{2}^{4}\int_{1}^{2}\int_{4} xy(z+2)dx dy dy \) Answer 120 Question \(y_{1}=\sin(6x)\)and \(y_{2}=\cos(6x)\) are the solution of the homogeneous differential equation \(y^{''}+36y=0\). Evaluate the Wronkian of the solutions Answer \(-6\) Question The functions \(y_{1}=e^{2x}\) and \(y_{2}=x e^{2x}\)are the solutions of the differential equation \(y^{''}-4y^{'}+4y=0\). Find the Wronskian of the fuction Answer \(e^{4x}\) Try Another Search