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4 years ago

PLEASE HELP DUE TOMORROW

Mathematics

2 answers:

maxonik [38]4 years ago

7 0

The answers to these questions are C and B

Whitepunk [10]4 years ago

3 0

C and b it would be

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First make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) x

e-lub [12.9K]

Answer:

$(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

$\int x ln(5+x)dx$

so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:

U=5+x

du=dx

x=U-5

so when substituting the integral will look like this:

$\int (U-5) ln(U)dU$

now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:

$\int (pq')=pq-\int qp'$

so we must define p, q, p' and q':

p=ln U

$p'=\frac{1}{U}dU$

$q=\frac{U^{2}}{2}-5U$

q'=U-5

and now we plug these into the formula:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int \frac{\frac{U^{2}}{2}-5U}{U}dU$

Which simplifies to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int (\frac{U}{2}-5)dU$

Which solves to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\frac{U^{2}}{4}+5U+C$

so we can substitute U back, so we get:

$\int xln(x+5)dU=(\frac{(x+5)^{2}}{2}-5(x+5))ln(x+5)-\frac{(x+5)^{2}}{4}+5(x+5)+C$

and now we can simplify:

$\int xln(x+5)dU=(\frac{x^{2}}{2}+5x+\frac{25}{2}-25-5x)ln(5+x)-\frac{x^{2}+10x+25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}-\frac{5x}{2}-\frac{25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

notice how all the constants were combined into one big constant C.

7 0

3 years ago

Find the area of the circle. round your answer to the nearest hundredth<br> area of circle= 2cm

cluponka [151]

Answeer:

12.57cm^2

Step-by-step explanation:

A=pi(2)^2

5 0

3 years ago

Read 2 more answers

How would u find the answer idk if they would still be the same and you just have to find that one missing angle?

ivolga24 [154]

Well... with the information you are given you just have to assume they are congruent triangles. The first picture looks like a right triangle, but the angle is 100 not 90... so it wouldn't actually look like that.

So for the missing angle all you do is 180= 100+ 55 + x

x=25

Then just match up the angles with the other triangle, they would be the same. K with F, J with G, and so on

8 0

4 years ago

The surface area of a plastic ball is 196 pi. A sponge ball has a radius twice that of the plastic ball. What is the surface are

IrinaVladis [17]

Answer:

Option C. $784\pi\ units^{2}$