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2 years ago

Sam guys different types of fruit in 3/4 pound baskets. Maria has 1 1/4 pounds fruit

Mathematics

1 answer:

Novosadov [1.4K]2 years ago

8 0

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Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

6 0

2 years ago

3, 1-을 6. + 9. 1-(급+음 12. 37 -27

umka21 [38]

Answer:

ohhhhhhhhhhhhhhhhhhhhhhhhh

6 0

2 years ago

The function f(x) is to be graphed on a coordinate plane.

gregori [183]

Answer:

f(x) is going to be on the y axis or intercept and what number it is on the line is in quotes f(x)="6"+2(1.05)^x it would be at 6 on the y axis.

5 0

1 year ago

What is the solution i need it fast!!!

zloy xaker [14]

Answer:

x < 3

Step-by-step explanation:

~Hope this answers your question!~

4 0

3 years ago

2(x + 4) - 5 = 3x + 3

OverLord2011 [107]

Answer:

x=0

Step-by-step explanation:

2(x+4)- 5 = 3x+3

Distribute

2x+8-5 = 3x+3

Subtract x values

8-5 = x+3

3 = x+3

Final Subtraction

x = 0

3 0

2 years ago

Read 2 more answers