Problem 13
Use Euler's Method with \(h=0.2\) to approximate the solution over the indicated interval. $$ y^{\prime}=x, y(0)=0,[0,1] $$
Problem 13
Perform the indicated integrations. $$ \int \frac{\sin \sqrt{t}}{\sqrt{t}} d t $$
Problem 13
Perform the indicated integrations. \(\int_{-2}^{-3} \frac{\sqrt{t^{2}}-1}{t^{3}} d t\)
Problem 13
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{2 x^{2}+x-4}{x^{3}-x^{2}-2 x} d x\)
Problem 13
Perform the indicated integrations. $$ \int \sin 4 y \cos 5 y d y $$
Problem 13
Solve each differential equation. $$ x y^{\prime}+(1+x) y=e^{-x} ; y=0 \text { when } x=1 \text { . } $$
Problem 14
Use Euler's Method with \(h=0.2\) to approximate the solution over the indicated interval. $$ y^{\prime}=x^{2}, y(0)=0,[0,1] $$
Problem 14
Perform the indicated integrations. \(\int \frac{t}{\sqrt{1-t^{2}}} d t\)
Problem 14
Solve each differential equation. $$ \sin x \frac{d y}{d x}+2 y \cos x=\sin 2 x ; y=2 \text { when } x=\frac{\pi}{6} $$
Problem 14
Perform the indicated integrations. $$ \int \frac{2 x d x}{\sqrt{1-x^{4}}} $$
