Problem 6
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int x \sin 2 x d x $$
Problem 6
Perform the indicated integrations. $$ \int_{0}^{\pi / 2} \sin ^{6} \theta d \theta $$
Problem 6
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{x-7}{x^{2}-x-12} d x\)
Problem 7
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. $$ y^{\prime}=\frac{1}{2} y ; y(0)=\frac{1}{2} $$
Problem 7
Evaluate the given integral. $$ \int_{1}^{2} \frac{1}{x^{2}+6 x+8} d x $$
Problem 7
$$ \text { use integration by parts to evaluate each integral. } $$ $$ \int(t-3) \cos (t-3) d t $$
Problem 7
Solve each differential equation. $$ \frac{d y}{d x}+\frac{y}{x}=\frac{1}{x} $$
Problem 7
Perform the indicated integrations. $$ \int \sin ^{5} 4 x \cos ^{2} 4 x d x $$
Problem 7
Use the method of partial fraction decomposition to perform the required integration. \(\int \frac{3 x-13}{x^{2}+3 x-10} d x\)
Problem 7
In Problems 1-16, perform the indicated integrations. \(\int t(3 t+2)^{3 / 2} d t\)
