Problem 11
Use Euler's Method with \(h=0.2\) to approximate the solution over the indicated interval. $$ y^{\prime}=2 y, y(0)=3,[0,1] $$
Problem 12
Solve each differential equation. $$ y^{\prime}=e^{2 x}-3 y ; y=1 \text { when } x=0 $$
Problem 12
Perform the indicated integrations. $$ \int \cos ^{6} \theta \sin ^{2} \theta d \theta $$
Problem 12
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int \ln \left(7 x^{5}\right) d x $$
Problem 12
Perform the indicated integrations. \(\int_{2}^{3} \frac{d t}{t^{2} \sqrt{t^{2}-1}}\)
Problem 12
Evaluate the given integral. $$ \int_{0}^{2 \pi}|\sin 2 x| d x $$
Problem 12
Use Euler's Method with \(h=0.2\) to approximate the solution over the indicated interval. $$ y^{\prime}=-y, y(0)=2,[0,1] $$
Problem 12
Perform the indicated integrations. $$ \int_{-\pi / 4}^{9 \pi / 4} e^{\cos z} \sin z d z $$
Problem 12
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{5-x}{x^{2}-x(\pi+4)+4 \pi} d x\)
Problem 13
Perform the indicated integrations. \(\int_{-2}^{-3} \frac{\sqrt{t^{2}}-1}{t^{3}} d t\)
