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OleMash [197]
3 years ago
14

Help please!integrate the following:

B3%7D%20%28x%29%20dx" id="TexFormula1" title=" \displaystyle \int \cos ^{3} (x) dx" alt=" \displaystyle \int \cos ^{3} (x) dx" align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
ArbitrLikvidat [17]3 years ago
4 0

Answer:

i think its help..............

koban [17]3 years ago
3 0

Answer:

\displaystyle  \sin  (x) -    \frac{ { \sin}^{3} (x)}{3}   +  \rm C

Step-by-step explanation:

we would like to integrate the following integration

\displaystyle \int  \cos ^{3} (x) dx

in order to do so rewrite

\displaystyle \int  \cos ^{2} (x)  \cos(x) dx

we can also rewrite cos²(x) by using trigonometric indentity

\displaystyle \int( 1 -  \sin ^{2} (x)  )\cos(x) dx

to apply u-substitution we'll choose

\rm \displaystyle u =  \sin ^{} (x)  \quad \text{and} \quad du =  \cos(x) dx

thus substitute:

\displaystyle \int( 1 -   {u}^{2}   )du

apply substraction integration and:

\displaystyle \int 1du -   \int {u}^{2}   du

use constant integration rule:

\displaystyle u -   \int {u}^{2}   du

use exponent integration rule:

\displaystyle u -    \frac{ {u}^{3} }{3}

back-substitute:

\displaystyle  \sin  (x) -    \frac{ { \sin}^{3} (x)}{3}

finally we of course have to add constant of integration:

\displaystyle  \sin  (x) -    \frac{ { \sin}^{3} (x)}{3}   +  \rm C

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The sides of △FGH are FG = 6 x+ 7, GH = 8x - 5, and FH = 10x - 11. If the perimeter of △FGH is 87, list the angles in order from
irga5000 [103]

Answer:

From largest to smallest: FG, FH, GH

Step-by-step explanation:

Given

FG = 6x + 7

GH = 8x - 5

FH = 10x - 11

Perimeter = 87

Required

Order the sides in descending order

First, we need to solve for x.

Perimeter of FGH is calculated as thus:

Perimeter = FG + GH + FH

Substitute values for FG, GH, FH and Perimeter

87 = 6x + 7 + 8x - 5 + 10x - 11

Collect Like Terms

87 - 7 + 5 + 11= 6x + 8x + 10x

96= 24x

Reorder

24x = 96

Divide through by 24

x = 96/24

x = 4

Substitute 4 for x in FG, GH and FH

FG = 6x + 7

FG = 6 * 4 + 7

FG = 24 + 7

FG =31

GH = 8x - 5

GH = 8 * 4 - 5

GH = 32 - 5

GH = 27

FH = 10x - 11

FH = 10*4 - 11

FH = 40 - 11

FH = 29

In order of arrangement in descending order, we have:

FG =31    FH = 29     GH = 27

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3 years ago
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Answer:

Hello! answer: 55

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