Problem 9
Plot a slope field for each differential equation. Use the method of separation of variables (Section 4.9) or an integrating factor (Section 7.7) to find a particular solution of the differential equation that satisfies the given initial condition, and plot the particular solution. $$ y^{\prime}=x-y+2 ; y(0)=4 $$
Problem 9
Perform the indicated integrations. $$ \int_{0}^{\sqrt{5}} 6 z \sqrt{4+z^{2}} d z $$
Problem 9
Evaluate the given integral. $$ \int_{0}^{5} x \sqrt{x+2} d x $$
Problem 9
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int t \sqrt{t+1} d t $$
Problem 9
In Problems 1-16, perform the indicated integrations. \(\int \frac{\sqrt{4-x^{2}}}{x} d x\)
Problem 9
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{2 x+21}{2 x^{2}+9 x-5} d x\)
Problem 10
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{2 x^{2}-x-20}{x^{2}+x-6} d x\)
Problem 10
Plot a slope field for each differential equation. Use the method of separation of variables (Section 4.9) or an integrating factor (Section 7.7) to find a particular solution of the differential equation that satisfies the given initial condition, and plot the particular solution. $$ y^{\prime}=2 x-y+\frac{3}{2} ; y(0)=3 $$
Problem 10
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int t \sqrt[3]{2 t+7} d t $$
Problem 10
Perform the indicated integrations. $$ \int_{0}^{4} \frac{5}{\sqrt{2 t+1}} d t $$
