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inn [45]
4 years ago
11

Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute va

lues where appropriate. Use C for the constant of integration.) x + 25 x dx
Mathematics
1 answer:
Ainat [17]4 years ago
7 0

Answer:

∫(x+25x)dx=13x²

Step-by-step explanation:

From Exercise, we want  calculate integral for x + 25 x dx.  

But this not required  a substitution to express the integrand as a rational function. We can calculte integral, and we get

∫(x+25x)dx= ∫x dx+25∫x dx=x²/2+ \frac{25}{2} · x^2=\frac{26}{2}·x^2=13x²

Therefore, we get that is  

∫(x+25x)dx=13x².

You might be interested in
Which expressions are equivalent to 2 (three-fourths x + 7) minus 3 (one-half x minus 5)? Check all that apply.
Mariulka [41]

Answer:

2(\frac{3}{4}x+7)+(-3)(\frac{1}{2}x+(-5))

2(\frac{3}{4}x)+2(7)+(-3)(\frac{1}{2}x)+(-3)(-5)

Step-by-step explanation:

The original expression given in the text is

2(\frac{3}{4}x+7)-3(\frac{1}{2}x-5)  (1)

And we want to check to what other expressions is equivalent. First of all, we solve it by writing explicitely each term:

\frac{3}{2}x+14-\frac{3}{2}x+15 (2)

Let's verify each of the other expressions separately. For the first one:

2(\frac{3}{4}x+7)+(-3)(\frac{1}{2}x+(-5))

We see that this is equivalent to expression (1), since the first half is identical, while in the second one, the combination "+-" can be simply written as "-", so we get

2(\frac{3}{4}x+7)-3(\frac{1}{2}x-5)

Which is equivalent to (1).

For the 2nd one:

2(\frac{3}{4}x)+2(7)+3(\frac{1}{2}x)+3(-5)

This is not equivalent. In fact, here we have applied the distributive property to each term: however, the 3rd and 4th term are not correct, because the (3) must be negative (-3), as in the original expression.

If we write it explicitely in fact, we get

\frac{3}{2}x+14+\frac{3}{2}x-15

Which is different from (2).

For the 3rd one:

2(\frac{3}{4}x)+2(7)+(-3)(\frac{1}{2}x)+(-3)(-5)

This one is equivalent. In fact, here we have applied the distributive property correctly. By solvign each term we get:

\frac{3}{2}x+14-\frac{3}{2}x+15

8 0
4 years ago
Read 2 more answers
Help me solve,Brainlist for first to answer
Vanyuwa [196]

Answer:

(i) the other two sides are 6 and  6\sqrt{2}

(ii) the other two sides are   \frac{4}{3} and                                         \frac{8}{3}

Step-by-step explanation:

(i)  Sine: sin(θ) = Opposite ÷ Hypotenuse

    Cosine: cos(θ) = Adjacent  ÷ Hypotenuse

    Tangent: tan(θ) = Opposite ÷ Adjacent

Here adjacent side = 6

opposite side = d

angle = 45°

other angles are 90° and 45°

tan (45) = Opposite ÷ Adjacent

 1 = d ÷ 6

∴ d = 6 × 1 = 6

so opposite side = 6

Hypotenuse ² = opposite side ² + adjacent side²

                      =  6² + 6²

                      = 36 + 36

                       = 72

hypotenuse = \sqrt{72}

                     = 6\sqrt{2}

the other two sides are 6 and  6\sqrt{2}

(ii) here adjacent side = 4√3

angle = 30°

other angles are 90° and 60°

opposite side = d

tan ( 30) = opposite ÷ adjacent

 \frac{1}{\sqrt{3}} = d ÷ 4√3

\frac{1}{\sqrt{3}} = d × (\frac{\sqrt{3}}{4})

                       3 d = 4

therefore d = \frac{4}{3}

therefore opposite side = \frac{4}{3}

Hypotenuse ² = opposite side ² + adjacent side²

                        =( \frac{4}{3})² +( \frac{4}{\sqrt{3}})²

                        = \frac{64}{9}

therefore hypotenuse = \sqrt{\frac{64}{9}}

                                     =\frac{8}{3}

the other two sides are   \frac{4}{3} and                                    \frac{8}{3}

7 0
4 years ago
You like math then here
Igoryamba

Answer:

-8b + 9 - 5k

Step-by-step explanation:

I am assuming the blue highlighted portion is your answer, and is not a part of the initial question

(-4b + 15 - 7k) - (6 + 4b - 2k)

Combine like terms

-4b - + 4b

Negative + Positive = Negative

-4b - 4b = -8b

15 - 6 = 9

-7k - - 2k

Negative + Negative = Positive

-7k + 2k = -5k

Put them all together:

0b + 9 - 5k

Simplify

-8b + 9 - 5k

I got the same answer as you (just in a different order)

5 0
3 years ago
What two numbers add to +5 and have a product of -3?
Tasya [4]
They don't come out even.
As rounded decimals, the two numbers are

<em>5.54138...</em>  and  <em>-0.54138...</em>


6 0
3 years ago
Which problem solving strategy would be best to solve this problem? How many different ways can you give change for 45 cents?
hodyreva [135]
I think A since working backwards and looking for a pattern wouldn't help, maybe C but im not sure
6 0
3 years ago
Read 2 more answers
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