Question

asked 2021-06-05

Given \(\int_{2}^{5}f(x)dx=17\) and \(\int_{2}^{5}g(x)dx=-2\), evaluate the following.

(a)\(\int_{2}^{5}[f(x)+g(x)]dx\)

(b)\(\int_{2}^{5}[g(x)-f(x)]dx\)

(c)\(\int_{2}^{5}2g(x)dx\)

(d)\(\int_{2}^{5}3f(x)dx\)

(a)\(\int_{2}^{5}[f(x)+g(x)]dx\)

(b)\(\int_{2}^{5}[g(x)-f(x)]dx\)

(c)\(\int_{2}^{5}2g(x)dx\)

(d)\(\int_{2}^{5}3f(x)dx\)

asked 2021-05-23

Find the indefinite integral \(\int \ln(\frac{x}{3})dx\) (a) using a table of integrals and (b) using the Integration by parts method.

asked 2021-04-23

Suppose that x represents the larger of two consecutive odd integers.

a. Write a polynomial that represents the smaller integer.

b. Write a polynomial that represents the sum of the two integers. Then simplify.

c. Write a polynomial that represents the product of the two integers. Then simplify.

d. Write a polynomial that represents the difference of the squares of the two integers. Then simplify

a. Write a polynomial that represents the smaller integer.

b. Write a polynomial that represents the sum of the two integers. Then simplify.

c. Write a polynomial that represents the product of the two integers. Then simplify.

d. Write a polynomial that represents the difference of the squares of the two integers. Then simplify

asked 2021-02-05

A differential equation and a nontrivial solution f are given below. Find a second linearly independent solution using reduction of order. Assume that all constants of integration are zero.

\(tx''-(2t+1)x+2x=0,\ t>0,\ f(t)=3*e^{2t}\)

\(tx''-(2t+1)x+2x=0,\ t>0,\ f(t)=3*e^{2t}\)

asked 2021-06-03

Evaluate each of the following integrals.

\(\int_{0}^{2}(x^{2}+2x-3)^{3}(4x+4)dx\)

\(\int_{0}^{2}(x^{2}+2x-3)^{3}(4x+4)dx\)

asked 2021-05-08

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

\(\int_{0}^{3}\sin(x^{2})dx=\int_{0}^{5}\sin(x^{2})dx+\int_{5}^{3}\sin(x^{2})dxZKS

\(\int_{0}^{3}\sin(x^{2})dx=\int_{0}^{5}\sin(x^{2})dx+\int_{5}^{3}\sin(x^{2})dxZKS

asked 2021-03-10

\(2x+4y=10\)

\(\displaystyle-{\frac{{{1}}}{{{2}}}}{x}+{3}={y}\)

Find the solution to the system of equations.

A. (0, -3)

B. (-6, 0)

C. There are infinite solutions.

D. There are no solutions.

asked 2021-04-02

Find all rational zeros of the polynomial, and write the polynomial in factored form.

\(\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}-{3}{x}^{{{2}}}-{2}{x}+{3}\)

\(\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}-{3}{x}^{{{2}}}-{2}{x}+{3}\)

asked 2021-03-03

Find all rational zeros of the polynomial, and write the polynomial in factored form.

\(\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}+{7}{x}^{{{2}}}+{4}{x}-{4}\)

\(\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}+{7}{x}^{{{2}}}+{4}{x}-{4}\)

asked 2021-01-28

(a) \(-2x + 3y = 4\)

(b) \(-2x + 3y = 6\)

(c) \(2x + 3y = 4\)

(d) \(2x + 3y = 6\)

(e) \(3x + 2y = 6\)