Problem 6
Use the technique of completing the square to express each trinomial as the square of a binomial. $$ 4 x^{2}-4 x+1 $$
Problem 6
Use a table of integrals to evaluate the following integrals. $$ \int x \cdot 2^{x^{2}} d x $$
Problem 6
Integrating a Discontinuous Integrand Evaluate \(\int_{0}^{4} \frac{1}{\sqrt{4-x}} d x\), if possible. State whether the integral converges or diverges.
Problem 6
Use the trapezoidal rule to estimate \(\int_{0}^{1} x^{2} d x\) using four subintervals.
Problem 6
Evaluate \(\int \cos ^{2} x d x\)
Problem 6
Find the integral by using the simplest method. Not all problems require integration by parts. $$ \int v \sin v d v $$
Problem 6
Evaluate \(\int \frac{x+1}{(x+3)(x-2)} d x\)
Problem 7
Integrating \(\int \cos ^{j} x \sin ^{k} x d x\) where \(k\) is Odd Evaluate \(\int \cos ^{8} x \sin ^{5} x d x\)
Problem 7
Use a table of integrals to evaluate the following integrals. $$ \int \frac{1}{4 x^{2}+25} d x $$
Problem 7
Use the trapezoidal rule with \(n=2\) to estimate \(\int_{1}^{2} \frac{1}{x} d x\).
