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3 years ago

Giving 45 points! I need help!

Mathematics

1 answer:

Monica [59]3 years ago

8 0

where is the question?

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Integrate this two questions

tankabanditka [31]

Simplify the integrands by polynomial division.

$\dfrac{t^2}{1 - 3t} = -\dfrac19 \left(3t + 1 - \dfrac1{1 - 3t}\right)$

$\dfrac t{1 + 4t} = \dfrac14 \left(1 - \dfrac1{1 + 4t}\right)$

Now computing the integrals is trivial.

$\displaystyle \int \frac{t^2}{1 - 3t} \, dt = -\frac19 \int \left(3t + 1 - \frac1{1-3t}\right) \, dt \\\\ = -\frac19 \left(\frac32 t^2 + t + \frac13 \ln|1 - 3t|\right) + C \\\\ = \boxed{-\frac{t^2}6 - \frac t9 - \frac{\ln|1-3t|}{27} + C}$

where we use the power rule,

$\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C ~~~~ (n\neq-1)$

and a substitution to integrate the last term,

$\displaystyle \int \frac{dt}{1-3t} = -\frac13 \int \frac{du}u \\\\ = -\frac13 \ln|u| + C \\\\ = -\frac13 \ln|1-3t| + C ~~~ (u=1-3t \text{ and } du = -3\,dt)$

$\displaystyle \int \frac t{1+4t} \, dt = \frac14 \int \left(1 - \frac1{1+4t}\right) \, dt \\\\ = \frac14 \left(t - \frac14 \ln|1 + 4t|\right) + C \\\\ = \boxed{\frac t4 - \frac{\ln|1+4t|}{16} + C}$

using the same approach as above.

5 0

1 year ago

Help please! Find x

zloy xaker [14]

Answer:

6√2

Step-by-step explanation:

A 45 45 90 right triangle, so ratio of leg : leg: hypotenuse = a: a : a√2 (a = value of leg)

Given: leg = 6

So the ratio of leg : leg: hypotenuse = 6 : 6 : 6 √2

Answer:

x = 6√2

6 0

2 years ago

Read 2 more answers

if the perpendicular drawn from any two vertices to their opposite sides of a triangle are equal prove that the triangle is an i

julsineya [31]

Go and answer yourself is going to benificial for you hdhdjdjdb

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Put you pen in your hand and hold it titely and put in your

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3 years ago

six candidates are running for two diffrent class offices. in how many ways can the offices be filled with these candidates

Bond [772]

Answer:

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on edg2020

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2 years ago

Solve the equation. Solve the equation. q+59=16 q+5/9=1/6

Anika [276]

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