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nexus9112 [7]
4 years ago
11

Integrate Sec (4x - 1) Tan (4x - 1) Dx ​

Mathematics
1 answer:
Delicious77 [7]4 years ago
5 0

\bf \displaystyle\int~sec(4x-1)tan(4x-1)dx \\\\[-0.35em] ~\dotfill\\\\ sec(4x-1)tan(4x-1)\implies \cfrac{1}{cos(4x-1)}\cdot \cfrac{sin(4x-1)}{cos(4x-1)}\implies \cfrac{sin(4x-1)}{cos^2(4x-1)} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~\cfrac{sin(4x-1)}{cos^2(4x-1)}dx \\\\[-0.35em] ~\dotfill\\\\ u=cos(4x-1)\implies \cfrac{du}{dx}=-sin(4x-1)\cdot 4\implies \cfrac{du}{-4sin(4x-1)}=dx \\\\[-0.35em] ~\dotfill

\bf \displaystyle\int~\cfrac{~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{u^2}\cdot \cfrac{du}{-4~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{1}{4}\int\cfrac{1}{u^2}du\implies -\cfrac{1}{4}\int u^{-2}du \\\\\\ -\cfrac{1}{4}\cdot \cfrac{u^{-2+1}}{-1}\implies \cfrac{1}{4}\cdot u^{-1}\implies \cfrac{1}{4u}\implies \cfrac{1}{4cos(4x+1)}+C

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Step-by-step explanation:

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Sveta_85 [38]

Answer:

z= 5/14

Step-by-step explanation:

Let's solve your equation step-by-step.

5−2(3z+2)=−4(1−2z)

Step 1: Simplify both sides of the equation.

5−2(3z+2)=−4(1−2z)

5+(−2)(3z)+(−2)(2)=(−4)(1)+(−4)(−2z)(Distribute)

5+−6z+−4=−4+8z

(−6z)+(5+−4)=8z−4(Combine Like Terms)

−6z+1=8z−4

−6z+1=8z−4

Step 2: Subtract 8z from both sides.

−6z+1−8z=8z−4−8z

−14z+1=−4

Step 3: Subtract 1 from both sides.

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Step 4: Divide both sides by -14.

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−14      -14

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3 years ago
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Answer:

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Step-by-step explanation:

We are told that the temperature may vary from 700 degrees Celsius to 1200 degrees Celsius.

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Let's find the average of the two temperature limits given:

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d_avg = 500/2

d_avg = 250°C.

Now absolute value equation will be in the form of;

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Ix - 950°C I ≤ 250°C

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