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3 years ago

I need help on my quiz!

Mathematics

1 answer:

Fantom [35]3 years ago

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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

3 years ago

Why is 1/8 cup equal to 1 fluid ounce

guapka [62]

Answer:

because there are 8 fluid ounces in a cup

Step-by-step explanation:

1/8 of cup = 0.125 cup = 1 fluid ounce

2/8 of cup = 0.25 cup = 2 fluid ounce

3/8 of cup = 0.375 cup = 3 fluid ounce

4/8 of cup = 0.5 cup = 4 fluid ounce

5/8 of cup = 0.625 cup = 5 fluid ounce

6/8 of cup = 0.75 cup = 6 fluid ounce

7/8 of cup = 0.875 cup = 7 fluid ounce

8/8 of cup = 1 cup = 8 fluid ounce

hope i helped

5 0

3 years ago

Please help !! i’m struggling

yaroslaw [1]

¿Aún necesitas ayuda? Podría intentar ayudar

3 0

3 years ago

One chicken is injected with a growth hormone while another chicken isn't. both chickens are wighed after a year

Margarita [4]

Answer:

weight

Step-by-step explanation:

The weight depends on the chicken

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3 years ago

1. Find the mass of each of these objects on the earth.

Orlov [11]

Answer:

hdhdujejeuhedudhdgdgdf egg ejeh

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2 years ago